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Lecture 28. What We've Covered: Course Summary
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well as they say all the things must come to an end and even those costs must come to an end today what I want to do is to summarize what we've covered during this course remind you of some of the important results leave obtained and give you an idea of how could continue your study in the future while we covered a lot of ground since the beginning of the lectures that's for sure I count over 700 slides that we've gone through and that's a lot of material for anybody and some of the material has been pretty advanced it's going to take you some time to digest and
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understand the material and become more comfortable with and the best way to get good at this kind of thing is to work through the problem if you work through a problem and you don't cheat and look at the answer and you struggle with it until you understand exactly how it works then you remember it for a good long time if you just treat as a flurry of facts that come and go but the problem is they usually go when you need them you can go back luckily in this format during these lectures online you can go back and review at any time and you can refresh your memory and that's 1 real advantage of the leverage that this kind of form gives us and just remarked that I Our treatment of Adams what at a much higher level I think many courses have time for that was partly a reaction to the kind of cursory treatment that our textbook date that material and partly the idea that there could be people who want to tune in and find out something who are in more advanced courses typically at this level and they can use that material to OK we had ,comma mechanics who was motivated by some early experiments Sciences about the trial and error basically that's the most powerful method inside and you've got to do an experiment and you've got to try to control all the things you can control so that you know that the things that you're changing her making a difference and that's why a good scientist records as much information about what's going on as is possible and we had several experiments that were really key 1 was very simple experiments of the distribution of radiation from a socalled black body like lampblack at temperature team which could be measure that distribution was simple it didn't seem to depend on anything except temperature and it was completely unexplainable by classical mechanics the 2nd key experiment was the photoelectric effect which again disagreed and seemed to indicate that life might have a particle nature that perhaps Newton's idea was correct and the 3rd was the doublesided experiment which seemed to indicate that electron could go through both slits but that's a more
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recent experiment and the earlier experiment was just that the electrons could distract from a nickel crystal and so that the electron seem to have a wave property because waste fractal particles do not and finally there was sweet we touched on briefly but there was just the stability of patents and chemical bonds both of which were very difficult to explain with classical mechanics and were left kind an unsolved riddle but so classical mechanics was floundering on all these fronts and whenever theory of knowledge is floundering that means that we have to think more deeply and winning that perhaps invented a new idea and this was of course an extremely exciting time but it was clear that the mechanics of the small so to speak was needed and that we could just extrapolate from our everyday experience with big objects when we go down to these very tiny particles as far as we can ascertain right now but quantum mechanics is basically completely unchallenged in the maintenance of flexibility in other words it's really a theory worth learning because it allows you to figure out things too many decimal points of accuracy and to explain all kinds of interesting phenomena and designed very tiny circuits that you can use of computers and so on and so forth and without it you're basically lost in any of those cases we talked about the matter and radiation in particular matter has a waiflike aspect quantified by the broadly wasteland and radiation hazards particle aspect which we saw when we don't don't the photoelectric effect this kind of way particle duality that in fact something can appear to have different properties depending on what you ask about the origin and allows us to explain all these experiments light photons injecting electrons essentially instantaneously from a metal surface and banking and electrons defecting from crystals the wave function we decided is the fundamental objects in quantum mechanics that's the thing that's common to everything and if we know the wave function then we know all that it is possible to know about the quantum mechanical system that means as a corollary that usually we do not know the way functions In in all its glory we only know some aspect of it depending on what we've chosen to measure but we don't know everything that is possible to know about most systems even very small quantum systems were trying to control it and all we can know there is the probability density or probability amplitude which is the way functions but what we measures the probability density and that's the fundamental thing and philosophically that's very frustrating to some people that when we prepare things in identical states often it seems like we get random results but there are many analogous things Thrower a died we get 1 through 6 and we get that grants and you could argue well the diet is not from the same way but if all 6 sides of the dog were identical so you couldn't see them when they were in your hand you couldn't see beforehand which we're going again then he couldn't tell which way it was when he threw it that appears as a number that that number appears to be random when you when you look at the state of physical systems is given by this way function which we capitalized and would put some Michael and dependent on time and it depends on the positions of all the constituents of the quantum system I'm classically there would be the coordinates of the particle although it kind begs the question if you're saying the coordinates of the particles that you think you know where they are but in fact what you're doing is treating this parameters in the wave function and the way function the fundamental thing when we make a measurement we represent that with linear termination operator and the only possible result of an ideal measurement is 1 of the I think values of the linear Hermitian operator which because its formation as real like that and once we make a measurement then the system has been altered usually by that measurement and less for measuring the exact same thing again in which case but we know the result we're going to get in that peculiar case because we've done experiment that rules out all the other probabilities and then if we do the same experiment again it's slight rather like throwing the dice on table images not throwing them again and just looking again what's up so you didn't give any chance to change and the set of all possibilities of these measurements just like the 6 numbers on the diet constitute a complete set they tell you everything that can possibly happen you can't have something outside that and that's very important because that means that we can make up a wave function as a linear combinations of the spike in states when we make the measurement we generally change the way functions and if we have 1st of all superposition whichever is here on slight 691 the sum over and see and finance and then we make a measurement we put on all had gone on united States financing and we get that I can dilute all and we know under measurements give a different Icahn value that the functions are thought which is expressed by the unique role of the product being 0 then after we obtain the result OK I am also OK the probability of obtaining that result is given by the square of the expansion coefficient K square on and after that the wave function has been irreversibly changed and now the wave function has changed to the Oregon State fights of care that seems to be kind of a collapse of probability because we had this big things the way function and we made a measurement and then collapsed and now it's in this state but of course but that might not be quite the right way to look at it might be a bit more complicated than that but you could ask exactly How does
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this Of the wave function happened and actually that someone opened a question like a lot of things and quantum mechanics the actual equations are not open to question but mechanisms and interpretations and reasons why certain things happened is open to question and some people temperamentally dismissed that as irrelevant and other people are quite interested in but for example suppose we flip a coin than before with little the chance of getting heads is 50 per cent but after we slept that actually make the measurement that the chance of getting heads it's only 100 per cent if we go ahead and that doesn't seem to bother us that there were 2 possibilities and now there is 1 we can have boosted the probability afterward back up to 100 per cent if we don't start doing other things with the coins and and so perhaps that's not so strange that the that we talked about uncertainty and went to operators don't commute that means incompatible and as measured by taking the difference in the order of the commentator and shown you commentator reminded you what it is for position momentum on its side each bar and that means that we can't measure those variables to arbitrary precision simultaneously 1 measurement causes the wave function change and then the other measurement is imprecise and viceversa and so you keep some sort of stepping on your own shoelaces over and over as tried repeatedly measure the properties where certain of this uncertainty there's been a lot written on the uncertainty principle which amounts to philosophy using the word uncertainty and somehow indicating that this is a very deep think that the uncertainty principle itself is just a technical detail concerning whether operators commuter not and whether measurements can be made arbitrary precision doesn't leave open huge up are unfathomable uncertainty about other things that kind of Miss USA of the word uncertainty and his nothing really to do with the principal itself I left along the way function will involving time according to the time dependent children here equation 8 chat site is equaled by each party citing the we really didn't really deal on this course with much time timedependent phenomena and that's where you could have a springboard into a more advanced courses is to look more deeply at timedependent phenomena what we did is we still that we I said Look we want to find out the property of helium atom or molecule or something like that that's left alone 1st what is it like in nature and what's the ground state and we know that there are left alone it's not changing it has certain properties is persisting in time and we call the stationary states and for a stationary stating the wave function changes phase which you can interpret as the shapes staying the same and it keeps changing color but the shape stays the same and the colors indicating kind but only square and we just figure out where the piles of sand are it's all the same so there's nothing we can actually see from that stationary state that's actually changing and the stationary states turned out to be the energy Oregon State and that's why solvent for the energy of the systems sold for because those states are the ones that have the staying power to persist in time and for the energy island states we can solve the equation exactly and we find that we just get complex exponential talents whatever the probability distribution at time 0 so the wave function changes faces I said and his and nothing else than you should think about changing color than we talked about bound states and quantized edition of energy but In arises somehow in the particles found in the reason that arises in the most fundamental reason is because the wave function has to fit into the space allocated to it and it can't come round for example on a ring and have a different phase than when it went around before it has a match up perfectly otherwise interferes with itself and more generally the wave function being away can interfere with itself and unless
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we have consists interference that remains constant time that's just cancel out 0 so we are going to see him so he could imagine some of the other energies not on the ladder of states that we derive as the solution to our equation could be there but there could be something wrong the way function may blow up and go to infinity so it's not normalizable is no proper probability or could cancel it could go around and could cancel itself out in which case it's 0 1 either 1 of those things skills and we found for apartment blocks that the letter states like and squared and there's 0 probability of being found outside the box on the other hand further gentler slope of the harmonic oscillator not so steep like a boxer but just squared then the levels when they like and they were all evenly spaced and that's a very clever that's very classic case study because it's simple to solve and we solved it and got the ground state being accounting functions and then the hydrogen atom is another 1 we can solve and hear the levels go light minus over and squares and again we have an infinite number of levels but there lowest 1 as they come up to some level that we call 0 there which is isn't isolated proton and electron at infinity but we have an infinite number of levels in there but they're within a finite ban yeah then we saw the particle could come through barrier so it could magically so to speak get around some sort of barrier and here on the other side as far as I am aware there is no experiment that tries to measure the transit in the barracks the particle is in front of the barrier and it comes out on the other side as far as I'm aware but we do find that particles do appear outside where they're supposed to be for example radioactive decay of an ounce of particles on the behalf particles part of the nuclear cement suddenly it appears out here because there a way function and there's some probability of being out there and finally it is out there and once it is out there and the strong forces not holding the 2 particles together it's ejected at top speed like about 5 million electron volts and that certainly would be allowed to see if you look at the barrier that you had to come over and had to squeeze through we call that totalling because the idea is that you don't have to have the energy to go over that period you can just somehow go through in classical mechanics this kind of behavior is just not allowed at all in Kwong mechanics it happens all the time In the last massive a particle is the more likely it is to come so Tomlinson very important for electrons and moderately important for hydrogen nuclei danger chat and pretty much diminishes improbability after that on the other hand if we have an unbalanced state they're free to go anywhere than the particle can have a continuous range of energy supply because the wave function doesn't have to fit into anything and then we've we derive that the wave function looks like a corkscrew corkscrew unless the right whether the momentum of particle is positive or negative and so but as I mentioned in some sense "quotation mark quantification always arises because the wave function has to fit somehow into a confined space free particles can just go anywhere it wants and doesn't have to have any face matching anywhere so it can have image this idea of "quotation mark authorization but emerges as a property of this theory it's not something we injected it emerges based on a fundamental hostility is 1 of the main triumphs of quantum mechanics because it explains atomic spectroscopy and a million other things that are very very important for everyday life and the classical mechanics completely trips up on then we talked about the approximate solutions to the shore equations we talked about perturbation theory and how to treat unknown solutions to the shrugging her equations and then an additional thing which we hope was small but sometimes it is small and we try it
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anyway and then sometimes we get kind of a difficult conundrum of the the reason we need things like perturbation theory is that sadly the equations that we have to solve it's difficult enough that we can only solve it for the simplest of ideal kind of model system we can't really solve exactly 4 other systems and so we have to treat them as approximate solutions but approximate in this game means as close as you like it's just me that we we can write in closed form the exact solution as fears the functions but we can write things that are very very close to many decimal point and luckily for us the hydrogen atom can be solved exactly and those solutions for STDs and so forth and 1 2 3 4 on those solutions guide our intuition about every other ad when we think about it to us orbital we can intuitively think will probably look something like that to us on hydrogen and then well as the nuclear charges shrink it down and then well it's not exactly the same because to us and another Adam may have 1 s inside and so things there be electron electric propulsion and so forth but we can't think in terms of this way and as I should be with the distribution functions the probability of finding certain electrons at positions they collect shells and so it is accurate to think of 1 to 3 year tail and so forth .period thinking about we can use perturbation theory than to correct any exact solution as long as we have a small perturbations but if we have a big perturbation with careful and then the other approximate method that's quite important that we used over and over again is to introduce a parameter into the wave function and optimize the parameter by adjusting it so that the energy is lower and that is a result of of the of the variation a principle which states that the where function that is closest to the ground state in energy is is better and so far we have it's a compass for us it's a way to know which way is north we have to have some measure when we're trying to change the way function and optimizes whether it's getting better and if the energy is going lower than it's getting better and if we have the exact way function for the ground state that we get the lowest energy possible and that that's very important that's our metrics forgot to tell you for doing the right thing we talk about atomic spectroscopy which follows a set of rules for dipole electric dipole allowed transitions dealt else plus or minus 1 Delta and its anything and so forth historically it's these emission spectra that led to the empirical relationship for emission lines being differences of 1 over and square which referred the formulated who knows how but anyway without knowing anything else he just seemed to say hey this is the 4th the 9 misses and my I mind is the 60 it was amazing numerical inside you do that but it was still completely I explained to what they were those differences but the quantum mechanics and came along and explained the host but that was a very important clues and we talked about term symbols which have the multiplicity to ask plus 1 where big guesses all the electron spins out up according to the rules of angular momentum is the orbital angular momentum of all the electrons and Jake is helpless asked which again follows the clutch Gordon series which goes down by 1 until it reaches the absolute value of our mindsets and those terms symbols are very contact way good to categorize and keep track of atomic transitions in things like sodium and other ads were we talked about the 2 yellow lines favorite close the 2 double P 3 adults and double P 1 both going to the double that 1 and we talked about atomic structure and what I would say Here's we did quite a bit this but a lot of atomic electronic structure calculations if you haven't figured it out already it involves a lot of integral and a lot of those in the girls are not so easy to do because they're multidimensional and girls and they have ugly things and and unless you adopt the right coordinate system they're completely hopeless to do is to try to do those in girls and Cartesian coordinate you make no progress at all you just end up with things that you can't and gray and although we
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didn't do it but we introduced elliptical coordinates but if we were getting serious about things like H 2 and H 2 plots and we could simplify our work a lot of willing to adopt that course system which I didn't do I just stuck with spherical coordinates for simplicity and a lot of hard work its simplest in these calculations to use atomic units atomic units are we measure energy and hot treaty and we set all the fundamental constants to 1 so that they're out of our hair and that that way we get nice simple equations like minus 1 dull squared and things like that that are much easier to write down and we've already got enough work doing all these minerals without having some gigantic fraction of it from that we have to he really writing all the time keeping track and then we remarked that there was a hidden advantage to doing it in these units and that is that when the calculation is so accurate that if you make a revision to 1 of the fundamental constants by doing a different experiments they change the value of each slightly really change the speed of light slightly out here and some decimal point but you don't want to have to redo everything all over but if you've done it in this these dimension was units you just automatically change the energy to update when you put in the new units and so you don't have to do it over because didn't "quotation mark in needy or kill
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jewels and that's much better because constant themselves can do sometimes get reply we did the hydride ion and and 1 thing we found out there is it's a pretty tough nut to crack you know in some senses the simplest to electron system it's hard because the electron electron repulsion which is between 2 unit negative charges and the attraction which is between a negative charge and a positive charge are about the same size and so treating the electron electron repulsion as a perturbation is treating something that's about as big as what said was big and small and what that I gave us unfortunately was an unstable situation where we predicted that the hydride and I would be unstable compared to hydrogen at and electronic infinity remember we got minus3 a monastery gates at rather than months half units than what we did is we expanded with our for our Greek friends say which now I'm sure you'll never forget this beautiful symbol and we expanded the orbital and allowed introduced that is a variation of parameters and we try to optimize that came darn close but unfortunately it was not stable and only a trial wave function where we say we hypothesize that we had 1 electron that was found rather tightly and another 1 was further out and then the opposite because for centuries you don't know which electrons which solely from you the possibilities when we took that went on that gave a reasonable result for height hydride is very big and I as I remarked it's bigger than fluoride and so it's not that stable and it's quite difficult to do by contrast feel when you introduce plus to charge then this interactions twice as big as this is an repulsion and boy that helps you a lot when you start to then we said Look we have that way function for hydride but that didn't consist of orbitals orbital is a 1 electron wave functions and we like to think of a multi electron wave function for an animal as a product of Oracle's and because we have 1 electron wave function what we do is we sneer out all the other electrons into just that cloud of charge according to the probabilities and that we treat that probability not as an instantaneous things like what's actually going on but it's something that's already completed and done and not dynamic and all it does then it's changed the potential energy that we solved we turn the crank we may need a computer a lot of integral whatever we have to to do and we optimize the 1 like electrons that we've got and then we put that money into the soup and smear out and we grab another electron out of the hat and we keep going around and around and around on a computer usually until none of the electron wave functions change none of the 1 electron orbitals changes from 1 to another and then in that case you can improve because if none of them change none of them are going to change if you go through again either and so at that point he quit and you say you've got a selfconsistent field solutions usually that solution is pretty good but it's never perfect and the reason this
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is because it neglects the fact that electrons tend to do in real life electrons would tend to avoid each other and that's called electron correlation and therefore theories that start with the selfconsistent field hockey Fox equations and then add correlations always give a better result if you treat correlation right OK then we talked about the the Pauli principle but the wave function should be antisymmetric if we exchange the labels which were calling 1 which were calling to for example and it's the other way function is factor Isobel if it factors into a spatial part time to spend part which often it does then if the spending power is symmetric spatial part is antisymmetric and vise versa this behavior we decided could be encoded in this new device called the Slater determinant because the Slater determinant when you change the columns rows permanently change assigned automatically and so it actually keeps track of this property for you not every wave function can be written as a single Slater determinant and that's 1 reason why we didn't do do a lot with open shell Adams and things like that there could be more complicated that we talked about molecules and in particular we introduced born Oppenheimer approximation which basically relied on the physical insight that the nuclei of being more massive moved slowly the electron move very rapidly and the electrons the 2nd the nuclei move a little the electrons immediately readjust their time to go around the track time and time again and they immediately readjust to whatever the new environment it's if they get squeezed out they get pushed out because the nuclei are coming together find the new clerical partner can hide in their final but they find the right solution essentially immediately there is no less and therefore it when we want us all that we can make an essential simplification we so all of a bunch of problems where the nuclei frozen and we just calculate the electronic energy and the Indian nuclear repulsion with everything frozen and that gives us an energy as a function of let's say to Adams moving apart and that is a very fundamental things understand about the way this thing because that frozen approximation as a function of big which was our into nuclear distance that's called potential energy curve or potential energy surfaces he has more than 2 months and that allows us to organize all our thinking about how the nuclear moved from now we so the electronic
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energy and won't want to figure out what the nuclear what to do we look at the electronic energy and we calculate forests and then we can see where the nuclear gonna move they're going to try to roll downhill to go too far either gonna roll up and so forth and so these curves and allow us to qualify and recall we had a couple of empirical curves that we introduced early on with vibrations Morse oscillator and even the LennardJones 612 potential the simplest molecule is H 2 Plus which we did in some detail and we could solve that under the born Oppenheimer approximation and we decided we could make up a molecular orbital which was the analogous 1 electron wave functions to an atomic orbital In except instead of just having 1 nucleus and solving 1 electron time we have to nuclei we solve on electron time wasted costs we can solve because it's only 1 electron the fact that the nucleus of splitter part isn't that
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big a deal that makes the math works but it doesn't doesn't change things in any other fundamental ways but only get to them we can Dennis too hot again because we've got to electron and most commonly than what we do is we start out with some atomic orbitals and we take linear combinations of the week that multiplied by numbers but we do not multiply the functions that's very important we don't raise them to powers or take square roots of summer do something else we just after we say a 50 per cent this 20 per cent fat and these numbers could imaginary parts is being "quotation mark mechanics after all but that's nothing worse than that and this is called the LCA all and all for linear combination of atomic orbitals molecular orbital approach whenever we start out with a certain number and of atomic orbitals we end up with the same number and molecular orbitals if we start out 12 we end up with 12 and and it's always like that and then we found we could classifier solutions bye cemetery and the lowest energy usually has the fewest notes and then as we go up things start increasing Nos things going to 0 in between the nuclei and very unfavorable things and those are the configuration of electrons the unstable for the molecules that's how molecules can disassociate Our rules for combining atomic orbitals the following day after similar energy that's because they have to have similar to broadly wavelengths in order to ensure that they have to have the same cemeteries and as I said in a more advanced course she'll understand exactly what that means when you started .period groups but for now just keep in mind that if 1 of them changes signed when he flip the molecule the other 1 doesn't those aren't going to interact the integral going to serious identically and then the 3rd condition is that they have overlapped in space because if they don't overlap and space at the hands of miles apart there's not going to be a molecular orbital possible they only have to be paralyzed so if you have more than 2 yeah I and bonding orbitals then build electron density in between the nuclear and bonding orbitals often put those between the the nuclear the Mets I tell however if the node is at the nucleus so and that it's not particularly bad it's just it's between In a bond but it's we saw a couple of examples that I highlighted where the molecular orbital theory was superior to the localized Fonda Lewis structured approach the 1st is that molecular oxygen is Parham magnetic the molecular orbital theory clearly predicts that we could have unparalleled because that's what we observe the other remembers called singlet oxygen and the other is that there are that
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we saw a simple example is that there 2 but for electron bands in the UV photo electron spectrum of methane 1 whom we called 1 and 1 of them we call T 2 and again molecular orbital theory predicted that these for bonds that we draw our really 3 plus 1 the 1 being rather different 1 remember being like that big teddy bear and the others had noticed but they didn't have knowledge between the bonds they had at the carbon nucleus itself and so they were net bonding made they include things together and the electrons 1 and those those 2 examples here to clear examples you can give where molecular orbital theory rather naturally predicts what we see and to go back and say Well I've got 4 sp 3 hybrids and drawings lines for bonds and so on and so forth but doesn't really explain and it's very very difficult to figure out how to going to explode and that's because it's wrong even it's useful in some cases then we had this thing the bond order is the difference between the number of bonding electrons minus the number and bonding electron divided by 2 and although we did emphasize that much there are nonbinding electrons nonbinding orbitals and those usually are a sort of like what you would draw was long hair on the Lewis structure and so they need occurred when nor helped you they are really involved in the active part the structure holding the ends together on and on we did a detailed calculations of the molecular orbitals for simple cases and what we found out what we did that is that the socalled exchange integral was the 1 that causes the body to be stable and that this change in a goal was basically purely quantum mechanical effect that was not possible would would not be seen in classical mechanics and that in turn explains how quantum mechanics naturally produces predicts that things like H 2 and H 2 0 and things like that are going to exist and beast more stable than the UN combined Adams but in classical mechanics this was just another conundrum to figure out we saw that are perfectly good LC AO and most solution for hydrogen molecular hydrogen H 2 sort of fell apart when we consider that the association of H 2 and to hydrogen and when we learn that that what we realize is that the molecular orbital approach assigns equal weight to a dissociating as H and NHS and hydride and age plus for proton and that was the problem there and by contrast the socalled valence bond approached the paper of higher in London the day the correct prediction that it would come and to have and what we realize that as we should keep our animal description when we've got the ball but we shouldn't assume that our description that we got with this optimize geometry is going to be the correct solution at all geometry and so what we have to do that is just are wave functions as we adjust are and the convenient way we did that was to mix in a certain amount of the Yantai bonding orbital as a function of all are and what we did that and optimized we got the correct prediction again we get the right ionization energy the right bond dissociation energy and we call this configuration interaction so we had to configurations to orbitals and then they were mixing and giving this interaction and activists the correct result and then finally we closed by talking about the localized system electrons pies system I think all organic chemists think of these kinds of Aaron socalled aromatic systems in terms of molecular orbitals so we dropped alternating single and double bonds but can never think of them that way they think of the localized system because the alternating single and double bonds doesn't predict the chemistry at all and when we feel that we get a detailed molecular orbital diagram and what we found out is that all the statement bonds world is full and then there were these 2 but were just half full so to speak in the middle and we could treat those 2 just looking at them just the P electrons in these alternate single and double bonds I'm just the same way as H 2 in other words the man with the same so why not just recycle and reuse and in the local approximation of what we did is we simplified but if we had a data system which is simplified we set on the overlap of an orbital itself is 1 big deal that means it's normalized and that we said the overlap of an orbital with its neighbor is 0 noted that seems to contradict the idea of forming a molecular orbital because they said they have overlap but keep in mind the overlapped s was usually just a correction term the denominator to us plus square U.S. plus 1 on 2 correct for the fact that you're losing some probability but it doesn't change the form of a solution the fact things move part is nothing much to do with the so it turns out that saying yes A 0 1 and still making a bond is OK because it's the other part that's making the bomb and you don't say is 0 so you have some energy terms we called Alpha and son and we said they're all the same for identical cars and some energy terms we call data the off diagonal once and then you can solve that and you find that cycling systems with foreign close to the high electrons are especially favorable when we get the same kind of thing for cycle you dying we predicted a dire radical instead because the 2 energy levels were the same that could be what happens or it could be be that the molecule distorts so that once but the benefits localized sponsored goes that because we get solid so here is the summary quietly contacts is really a deep and very beautiful descriptions of atoms and molecules it certainly isn't easy but it's not impossible leader and most of it comes down to just having enough knowledge of mathematics so you can understand what the equations are on house and console and then once you reach that level then we can focus on what it means and you can understand what it means in terms of science and chemistry and not be lost in details certain aspects of quantum mechanics sites remain hard to understand for example that if you want the concrete explanation of exactly how electron goes through both slits at once and that's very difficult I don't think anybody can give you an explanation of that because for 1 thing the only time does that is when you don't look and if you don't look quite mechanics is you don't really know what's going on and so you can proposed some mechanism by which you have no experiment to measure in quantum mechanics you have to propose an experiment that measure something and when we measure that we find out about it once you definitely once lived the other so if we have the possibility of measures if we don't measure that both both possibilities are entertained simultaneously nevertheless even the interpretation or some features of this theory can be hard to understand and terms of everyday behavior of objects when it comes to calculating atomic and molecular properties when you need to get something right this theory unparalleled it seems to be an extremely accurate and versatile theory and you can do lots of work with and I would say In my experience quantum mechanics remains completely unchallenged In the small world I hope you enjoyed the topics we've covered and I hope that you go on to learn more about chemistry and science banks
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Diethanolamine
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Klinisches Experiment
Origin of replication
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Ice front
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Optische Analyse
Caffeine
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Thermoforming
Stiffness
Atom
BoyleMariotteGesetz
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Mineral
Thermoforming
Atom
Host (biology)
Calculus (medicine)
28:36
Semiotics
Sense District
Hydride
Sunscreen
Cell nucleus
Atomic orbital
Solution
CHARGE syndrome
Wursthülle
Man page
Fluoride
Klinisches Experiment
Electron
Atomic orbital
Mortality rate
Crack cocaine
Potenz <Homöopathie>
Surface science
Sense District
Hydride
Gemstone
Chemical property
Action potential
Lightning
CHARGE syndrome
Solution
Functional group
Atomic orbital
Optische Analyse
Pan (magazine)
Atomic orbital
Nucleolus
Atom
Isotopenmarkierung
35:53
Reaction mechanism
Chemical bond
Atomic orbital
Solution
Lewisite
Linear combination of atomic orbitals
Atomic orbital
Molecule
Electron
Combine harvester
Mortality rate
Oxygen
Metastasis
Molecularity
Potenz <Homöopathie>
Cell nucleus
Chemical bond
Lightning
Fat
Solution
Oxygen
Disease
MOTheorie
Combine harvester
Sample (material)
Functional group
Atomic orbital
Optische Analyse
Azo coupling
Chemical structure
Atomic orbital
Methane
Nucleolus
40:32
Chemical bond
Solution
Chemistry
Alpha particle
Molecule
Electron
Stratotyp
Hydride
Doppelbindung
Elektrolytische Dissoziation
Chemical property
Cell nucleus
Topicity
Gold
Wine tasting descriptors
Electronic cigarette
Solution
MOTheorie
Systemic therapy
Emission spectrum
Locus (genetics)
Thermoforming
Calculus (medicine)
Bearing (mechanical)
Ageing
Reaction mechanism
Atomic orbital
Organische Verbindungen
Wursthülle
Lewisite
Aromaticity
Lone pair
Ionisationsenergie
Methanisierung
Active site
Atom
Configuration interaction
Body weight
MetallmatrixVerbundwerkstoff
Molecularity
Deep sea
Nitrogen fixation
Carbon (fiber)
Chemical bond
Protonation
Hybridisierung <Chemie>
Man page
Chemistry
Hydrogen
Valenzelektron
Functional group
Chemical structure
Atomic orbital
Atom
Metadata
Formal Metadata
Title  Lecture 28. What We've Covered: Course Summary 
Alternative Title  Lecture 28. Quantum Principles: What We've Covered: Course Summary 
Title of Series  Chemistry 131A: Quantum Principles 
Part Number  28 
Number of Parts  28 
Author 
Shaka, Athan J.

License 
CC Attribution  ShareAlike 4.0 International: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  10.5446/18906 
Publisher  University of California Irvine (UCI) 
Release Date  2014 
Language  English 
Content Metadata
Subject Area  Chemistry 
Abstract  UCI Chem 131A Quantum Principles (Winter 2014) Instructor: A.J. Shaka, Ph.D Description: This course provides an introduction to quantum mechanics and principles of quantum chemistry with applications to nuclear motions and the electronic structure of the hydrogen atom. It also examines the Schrödinger equation and study how it describes the behavior of very light particles, the quantum description of rotating and vibrating molecules is compared to the classical description, and the quantum description of the electronic structure of atoms is studied. Index of Topics: 0:05:11 Matter and Radiation 0:07:33 Postulates of Quantum Mechanics 0:10:11 Measurements 0:12:11 Uncertainty 0:13:36 Time Evolution 0:15:37 Bound States 0:17:56 Tunneling 0:19:49 Unbound States 0:21:06 Approximate Solutions 0:24:28 Spectroscopy 0:26:19 Atomic Structure 0:33:05 Pauli Principle 0:34:11 Molecules 0:42:25 Chemical Bonds 0:43:17 Dissociation 0:45:04 Delocalized Systems 