New Revolutions in Particle Physics: Basic Concepts | Lecture 7

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New Revolutions in Particle Physics: Basic Concepts | Lecture 7
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(November 13, 2009) Leonard Susskind discusses the theory and mathematics of angular momentum.
Theory of relativity Ruler Kickstand Hypothetisches Teilchen Schubvektorsteuerung Order and disorder (physics) Access network Angular velocity Zeitdiskretes Signal Continuous track Leistungsanpassung Star Weather Angeregter Zustand Reference work Cylinder head Measuring cup Combined cycle Composite material Drehmasse FACTS (newspaper) Kopfstütze Classical mechanics Spant Finger protocol Sizing Direct current Spin (physics) Universe Video Cartridge (firearms) Mass Rotation Line segment Orbit Restkern Spinning (textiles)
Quality (business) Schubvektorsteuerung Day Measurement Magic (cryptography) Angular velocity Particle Apparent magnitude Band gap Canadair CL-44 Electricity Angeregter Zustand Typesetting Speckle imaging Electron Combined cycle Ballpoint pen Minute Drehmasse FACTS (newspaper) Sizing Direct current Spin (physics) Hour Plant (control theory) Electronic media Mass Rotation Restkern
Ruler Funkgerät Cosmic distance ladder Schubvektorsteuerung Measurement Multiplizität Particle Bird vocalization Canadair CL-44 Negation Nanotechnology Wind farm Mail (armour) Truck Mechanic Electron Electronic component Single (music) White Drehmasse FACTS (newspaper) Classical mechanics Cogeneration Kopfstütze Direct current Sizing Fahrgeschwindigkeit Mass Rotation Orbit Natürliche Radioaktivität Movement (clockwork)
Ruler Hot working Schubvektorsteuerung Day Measurement Order and disorder (physics) Force Spaceflight Screw thread Particle Continuous track Limiter Cardinal direction Wednesday Spare part Rail transport operations Hose coupling Angeregter Zustand Quantum Cylinder head Mechanic Tool Cut (gems) Combined cycle Committee Electronic component Year Composite material Single (music) White FACTS (newspaper) Classical mechanics Cogeneration Spin (physics) Direct current Rocket Plant (control theory) Electronic media Book design Noise figure Miner Movement (clockwork) Firearm
Theory of relativity Ruler Day Measurement Particle Watch Bird vocalization Roll forming Video Rail transport operations Mail (armour) Star Angeregter Zustand Photodissoziation Blood vessel Combined cycle Key (engineering) Electronic component Car seat Year Power (physics) Pair production FACTS (newspaper) Kopfstütze Finger protocol Angle of attack Spin (physics) Gentleman Direct current Annihilation Hour Movement (clockwork) Last
Mechanical fan Hot working Quality (business) Formation flying Winter Ballpoint pen Nuclear reactor Year Hot isostatic pressing FACTS (newspaper) Specific weight Bird vocalization Annihilation Turning Band gap Gentleman Ship class Relaxation (physics) Bow (ship) Spare part Tretboot Rail transport operations Week Last
Theory of relativity Ruler Funkgerät Hot working Quality (business) Hypothetisches Teilchen Day Galaxy Bill of materials Particle Kette <Zugmittel> Night Basis (linear algebra) Roll forming Bahnelement Ship class Spare part Musical ensemble Controller (control theory) Angeregter Zustand Quantum Fuel Cylinder head Bus Measuring cup Combined cycle Electronic component Year Automobile platform Railroad car Map FACTS (newspaper) Kopfstütze Direct current Spin (physics) Sizing Wear Hour Commodore MAX Machine Book design Hochfrequenzübertragung Wind wave Bleisatz Punching Ground (electricity) Last Firearm
Ruler Kickstand Day Spaceflight Wire Particle Basis (linear algebra) Bird vocalization Phase (matter) Ship class Veränderlicher Stern Spare part Musical ensemble Angeregter Zustand Electron Augustus, Count Palatine of Sulzbach Flat engine DVD player Electronic component Year Tuesday Map Hot isostatic pressing FACTS (newspaper) Metal Gentleman Cartridge (firearms) Signal (electrical engineering) Steering wheel Van Rotation Miner Week Movement (clockwork) Firearm
Cooling tower Neutron Electron Evening Day Order and disorder (physics) Lead Ozone layer Positron Ship class Spare part Musical ensemble Video Restkern Angeregter Zustand Superconductivity Fuel
Cosmic distance ladder Hot working Electron Year Rolling-element bearing Railroad car Bird vocalization Serientor-Sampling-Leitung Particle shower Cartridge (firearms) Cardinal direction Angeregter Zustand Quantum number
some steam university wilderness
tallied tonight is angular momentum after it is 1 of the most
important interesting aren't intuitive thing yet very very simple aspects of elementary particles or anything else for that matter this been there in angular moment of let's 1st talk a little bit about what angular momentum cases but let me like a pretend for moment Pitino angular momentum which you probably do but maybe you get a rough idea it's got to do with how fast the system was rotating in Helmetta in that's sort thing angular momentum is 1st of all a vector quantity . 7 direction the mathematical definition of the angular momentum is its direction as a vector points along the axis of rotation that kind of obvious armed is unlikely and ruled the system's rotating about access you don't know offhand definition whether the angular momentum pointing that way or that way Michael duels along the axis so role the right-hand role of its rotating that way you wrap your fingers around the direction rotation found points along the direction of the angular momentum that's not something you pull that something you define the direction of angular momentum at built up out of the romance the speed of rotation that sort of thing the moment of inertia to be exact which is a combination of the match size of the system and the loss to angular velocity and any system anyway ordinary system composites from this the cup he made about a lot of Adams and actually can have 2 kinds of angular momentum was called orbital angular momentum and the all underlying the momentum is a consequence Of the motion of its end the romance it could be angular momentum angular momentum 1st of all is relative to particular acts as an object is moving around the access it has angular momentum relative tobacco taxes even as the the thing is is not itself not spending of words spinning spinning means rotating about some internal it has angular momentum by virtue of the fact that it's moving Ovitz a circular orbit around my head I see it as annual momentum that the angular momentum were interested in the orbital angular momentum and angular momentum orientalist is the angular momentum of speed so as spin angular momentum the spin angular momentum is what ever angular momentum would be there in a frame of reference weather system was a rash of this system as arrest the only thing where the center of mass of the system is rest I don't mean that it's not rotating I mean that center Messer standing still in the frame of reference words momentum is 0 ordinary moment from any leftover angular momentum called they basically our nails who said a bastard or something that's been birth just to illustrate nearly an orderly thinking about things you can take a basketball and you could start a rotating that's the same thing that's the same object as the original basketball which was a rotating except the rotating if we also keep track of the fact that quantum mechanics the amount of angular momentum is discreet you can't interpolate continuously between different angular momenta then you could ask the question as it becomes a death question of definition that his at an object with a little bit with no angular momentum and the new rule will take up you spin up and give it some angular momentum is the same object rotating or is no object now that obviously a matter of definition but In practice the real issue is how much energy does it take descended into rotation now you say I consider the smallest amount of rotation arbitrarily small amount of rotation and so it takes arbitrarily small amount of energy to start rotating but that's in classical mechanics you have a continuous interpolation between the thing not rotating and the thing rotated but a quantum mechanics you don't have a continuous interpolation and so I would say it's a matter of definition whether you want to think of the EU rotating nucleus as the same object discreetly different object but the real question there said unions How much energy does it take the star system and rotation given that the rotational states of discrete and makes sense how much as much energy doesn't take the stand until the 1st excited state 1st the amount of rotation you've inject it is very small normally takes a little bit of energy then the object is probably pretty
recognizable as the same object as when I was rushed but it takes an enormous amount of energy but could take so much of the summit imaging blow the system of apartheid so for example our can add it is further you we try to set Adam into rotation with too much or angular momentum the electrons will just fly off and we so you certainly make 53 distinguishable different when you set them interrupt kitchen and discreetly difference 1 on electronic Kenya set an electron forget for a moment that the electrons has intrinsic spin for a minute but forget that for a minute piece set an electron in the rotation so that resembles the same object except rotating about some hours or is electrons somehow so small and so point like that it doesn't make any sense the rotation a thing which is infinitely small simple point for simple math point it's hard to conceive of at least my usual mental pictures of setting a thing into rotation but of the electron electrons infinitely small maybe the electron is not infinitely small Our here is not the only small maybe we have a chance of scene of rotating so the question becomes how much energy does it take the set of electron into rotation now the initial tends to depend on the size of an object forgiven it depends on the size of an object surprisingly maybe it surprisingly it's not surprising the smaller of the object more energy Texas 7 rotation big objects to consent from a very small angular velocities small objects take larger amounts of energy to excite him forgiven amount of rotation forgive amount of angular momentum electron maybe so small that it probably is known to be so small that they energy that it would take to give it 1 more unit of angular momentum would be astronomical would be maybe the plant energy your some him large energy and so we don't see each in a laboratory rotating electrons and sank the rotating electron may be so different from an ordinary electron would need quality Elektra art up some of this is that when we talk about objects and quantum mechanics we owners or particles in particular nuclei on any simple systems relatively simple systems they have aII amount of angular momentum which characterizes them and which once and for all is fixed you don't talk about electrons with different angular this difference in angular momentum in the angular momentum of electron is always the same if it has any angular momentum at all and that well just because of that had more angular momentum Yukon different object now angular momentum was said was a Vivek day remove define exactly what the defining moment but said that there it has only the length of the vector was proportional permittees speed the rotation so forth taken point in any direction Webb Lees classically Hickam point in a new direction shall we think of 1 thing angular momentum of an object and different directions as corresponding to different objects but suppose we now do have an object which has some angular momentum we call it what you would call upon lecture serve what and try and try and try to stand trial identified as enshrined his angular
momentum pointing that were candy angular momentum point another direction well yes it better be able to because the laws of physics are rotationally invariant there's nothing special about 1 axis another axis so yes the same object can be rotate in a different direction even if it can be made to rotate with more total angular momentum solve pointing it in different directions we would say corresponds the same object if an electron does have angular momentum and we should be able to think of that angular momentum in a new direction on the other hand the amount of angular momentum the magnitude of it is quantized and sold as a set of our we get gap to the 1st excited state of electron may be so large that we would column electric buckets of the angular momentum and point direction is quantized knowing have to enter into a theory angular momentum tonight will go to those of mathematics of angular momentum and is silly magical it's magical and it seems talk only abstract totally on intuitive and then experimental of facts and predictions and the entire properties of Spain as an experimental LONDON observational facts about particles that yet question are located you know what they know at the moment of inertia of an object is OK of the question of the simplest as it is counterintuitive a little bit throughout on the moment of inertia is a combination of media and the mass of the object and the radius of the object ball or some sort of its and squared now it depends on the details shape of the object and depends on how the matter is distributed sometimes rid 3 have Zamora square with its border more square that's call the moment the most we energy of a rotating object refer votes for now then there is the angular momentum to the angular momentum of the
object is made up of the object but say the Alabama River object say moving with velocity v then roughly speaking order of magnitude the mass times of varsity that's the
ordinary momentum of a piece of its nest on velocity multiply that by all our bats a batch angular momentum momentum at times distance is angular momentum of a momentum of Soviet times the distance from the center of the angular momentum and if you write them the kinetic energy kinetic energy is 1 he FMV squared what you'll discover is angular member the squared
provided by the momentum and twice a moment of inertia to be exact so that's the energy the kinetic energy of rotation busy angular momentum squared divided by twice the moment of inertia now forget it may at what say the massive of electron small it is the smaller the moment the romance of the moment of inertia goes in the denominator and that means the amount of energy that it takes to increase angular momentum by 1 unit is inversely proportional to the square of the size of the object truck or at a classical mechanical fact the only thing that comes newly in Quanah mechanics visibly angular momenta discreet discreet but the fact that have forgiven angular momentum a small object cost more energy that's classical mechanical fact OK let's of what do some mathematics but I would really under the mathematics Emmanuel movement it's both totally on intuitive and simple simple enough and is a great example always see extremely abstract mathematics which Yukon suddenly popping out the heard on tour of answers but nevertheless experimental Alexa let's begin well 1st of all let's begin with a single particle emitting sent circular orbit for simplicity the angular momentum is the momentum of the particle times a distance from the origin of mass times velocity times distance call momentum Betsy angular momentum in this very simple context our positive or negative that depends on the sense of rotation going this way I think they're called positive going that way of Kong negative but threat its number important Betsy angular momentum point after now this object has momentum as angular momentum be has momentum as momentum because of his velocity so this is not yet Spain but now supposing we had Top particles at opposite ends of diameter here both going with the same sense of location and now the center of mass would be arrest the sentiments of system would be arrest buddy angular momentum would certainly not be 0 will be the sum of the 2 angular moment then they're going in the same direction so he is an example where the center a mail service system commute rest but still angular momentum the suspended why Mallette said they knew little more refined precise definition Our angular momentum I said before angular momentum as a back vector there and that means Oravetz noted by putting a little over top of it momentum as a back there and also spatial location is a special location of an object in his relative told origin relative to more knowledge and we can call it of vector it's the radio vector but some of the components 1st before we get onto an angular momentum of the components of the olive sector I just the coordinates of the position of particles of the components of all our sorrow over here the threat over here component of our farm jobs ex-wife is 80 X Y and Z being the coordinates of a Europe opposition particle Marsalis sometimes call them X 1 X 1 x 3 x 3 being Sieck still being why X warned being next OK so we have these 2 actors somehow the angular momentum a product of the 2 vectors the angular momentum is itself a vector how do you make of vectors of 2 vectors by multiple by multiplication what kind of rule multiplication is that takes 2 vectors and combines them together by some old multiplication to make Novak resigned that there is only 1 role with only 1 such World II and that surpassed product across product and the fact is an ambiguity is not cross POP croissant that's a question of whether you're right here and a left-handed use right him will have left him our standard convention is that are crossed peek at an fiddle remember that is right here before left and remember we we could figure it out from want across but we who labeled the call admits of ER sector is also the p vector p vector also has coordinates and its coordinates are P. XQY in PC or P 1 B to be free it was a lot of from pension now I can ask What are the components of the angular momentum of that all you have to know is how to build but the the most film everybody knows build across products or just below it is along also the x component of the cross but IPX component of the angular momentum is a white component of position kind of busy component of momentum might best be Z component of position times the white component our momentum this is the only 1 that I ever remember telex Eagles wide and HP's each time I read that off the other 1 here I know that I have to put them in the upper change HP's EPA's P white wine and then I want to go down from LX a white males I
never remember them but all the you just cycle from next busy and backed extra like figure ex-wife media as being a point clocking you go from 1 the next so your from X Y Y ghosts egoist X from X 1 y z X is synonymous with the formula Z X Y P 1 minus X PC minus PX the only reason I should emphasize the cycling is to keep track of the signed howling although wives and expertise winners each PX appeared at the cycle forever and the that's a component of angular momentum of a point particle moving in the vicinity of some origin Of course it's all a bit of angular momentum of that part was not the spin angular movement to make us then angular momentum for a system of ordinary in classical mechanics maker spent angular momentum in that have a lot of particles that leads to anywhere so Javanicus spin angular momentum with 2 of you have to have several particles to being a part several I had you build the angular momentum or composite system you just a and B angular momenta as vectors UN them as sectors you and the angular momentum of all the constituents want you and angular momentum and then you could have a spin with a total momentum is equal to 0 but the angular momentum is not equal to 0 but this is a basic formula for a single indivisible point particle and as I said you just a for us a lot of particles next step we want to to do the quantum mechanics of angular momentum this is the classical mechanics accurate also the acquired mechanics but to get the quantum mechanics they basic mathematics of quantum mechanics is the quantum mechanics of operators also quantities of physical significance meaning to say things that you could observe measure also things Our represented in quantum mechanics by white operators mission operators operators and say there's no special exception moment that the components of angular momenta amid represented by operators but that figure out what those operators are all you really need to know is what they operators which represent our position and momentum are in fact we don't even really have to know very much about may have detailed property of the position and momentum operators all we have to know is there commutation relations with their commutation relations at all we need to know in order to carry on and work out everything so what what is it means whether the implications of tool operators commuting with suppose i've to operators which represent 2 observable quantities these 18 this and the Venus of assistant and I know that AT&T commute what does that tell me about the observation yet exactly you can simultaneously measured what if they don't commute didn't make you can simultaneously measurement the most famous example of 2 things that you cannot simultaneously measure of course it is position and movement the implication is that in quantum mechanics operators represent things where erased P 1 featuring on the 1 hand X 1 X till it actually commuter among themselves so what on the right commutation I'm not to some extent is a possibility of quantum mechanics to find them in the 1st chapter of direct book basically a possibility if you like but there are no limitations on what you could write them but wouldn't take was passed 1st postulated is that you can simultaneously measure of all 3 coordinates Of position is no limitations on how well you could determine the x y and z coordinates a position that all simultaneously measurable and the implication of that is that every X commute from memory of another X come right that down acts I X J E equals 0 for all while I in jail all are injured incidentally anything commutes with itself very weird or something didn't Camila itself valid so you could measured but to could measured simultaneously with self idea OK so commits itself seems thing for moment that there is no limitation on being able to simultaneously measure the different components of movement salt PIE PGA equals 0 what about X is with E that's exactly what the uncertainty principle is about it tells us that we cannot simultaneously measure coordinates position but let's admits in which position can which component can we not measure simultaneously any answer that this is not a lot of freedom about this but nevertheless a ribbon to stay was a postulated that X 1 and P 2 committee simultaneously measures be X school in the article in component of words momentum are not limited by the uncertainty principle it's x component position and the x component of momentum which I'm not simultaneously measurable so we have that X with P X is not equal to 0 better and more musical I it's small wiII because we don't
expect a macroscopic big every object to work to you down with is all you do is small when you make when you the Fox after and so forth for y and z Zoellick right down a general formula but the commutator of X I would P. J is I H. Clark a fight equals J and 0 if I doesn't today is a clear and represent that before the chronic Delta here and a nice were systematic rape to describe properties position that an alternate all we really need to know in order to in order to understand the properties of angular momentum and local understand the properties of state but there's 1 other point of that worth emphasizing that angular momentum has units of plants constant howling that while angular momentum as units of distance times momentum Our years distance time momentum on the right side the plants constant and also a cut of course and the uncertainty principle got the X Delta P is greater a equal to whatever some number times plants constant you see that wants constant has yielded only times momentum and angular momentum has units of late so completely surprising that angular momentum is quantized new parts constant harbinger of basic quantum in nature which is part of really we have got point about what I wanna work out for you is the commutation relations of the of angular momentum will find out that once would work out the commutation relations of the angular momenta components of the angular momentum we can't forget that lofty anymore it's just the components of the angular momentum whose commutation relations we want desolate still let's 1st compute the commutator of LX with White the number of hard I'll happily a little bit because I haven't I have to remind you with all the rules about the algebraic rules of Conde patents are but a simple a simple enough that that because were actually want to cut it head of With white elects a little wife his wife easy the commutator of white easy miners TPY that's a 1st Our entry into country but urged the commuter British force LX want which is Zeke at minus X figure molest 24 research firms 3 of the work force 1st Carver West might would be 30 people who fail the the course showed up where he another he is sigh yeah they may be a sign that right why while there are that Olivier like now not firms was right at the father of 2 Wickham figure this out I want to wiping but for that accommodate up this can Of the 1st factory with this terms 2nd back there is nothing to prevent y you know when you take a look summit it is a thinking about pushing up operators through Rita canny freely pass through each other without a change in the value of of the offer I'm nonwhite commute elects so can likeness Dexter also computer commutes with these please easy commute to X and easy commute pleasing so you compose this 1 right through this 1 North so these 2 commute with each other contribute nothing the commutator another combination the Swansea yuppies what that these 2 also commute each other deletes don't with each other what compare this and this and this will the daily work it out arm we have a white easy Z acts only thing which doesn't commute here Wednesday so I thinking that the answer is just what kinds of just why columns he acts it doesn't matter which Saudi right and down White Pines he acts and then there's the commutator please EU would what the commutator appease you would be at sorry for what a minor solute it can't get top auditing side committed with symmetric meaning when you change the order were to write the rocket the changes are we be interchange which parts of this this kind later on PC with minus I thought him this guy over here with us from where he was a really PYA next year I lost my mind a couple of days at sea with easy and that shiite borrowed from another all of it that's while along these are 1 x these EXP what remind in each other but we always you want want to he I believe it is our next thing I was but last want for next year is so we learned they would by our age far goes but what kind
of pretty that community all of that you get back the only thing you have to do anything about it he said recombination close yeah I call out Is it which that remember where means said let's go online but they decide reporters horizontally but by Boris N. that ex-wife why but I'll all L C O 1 those the who our relations on which the U.N movement that that tells you how many articles it then you find that it doesn't matter they are many articles and it could be many particles in the rest restoration of the U.S. at the on that on Star on my very special about the way the all all of it could be as you want at along direction were on that as long as there usually are they won't be good he's war give me a call back there in in 1 you confirmed he saw principle we could work out condemnation of the components of angular momentum in some of the that what finding is exactly the same more or less the same form taxis that I was surprised Nowhere is becoming less than location the he warned that that can easily fuel from Italy will be in the independent observable we ended taxes we choose to work the man but I didn't preference is the the spin off to visit where erection it also millionaires there will be usually abstract Matt much horror are leading him don't let it get I think I have a report floating and then grind down all possible your power most of it becomes matter back while a lot finally something dressed up as a key don't fossils get a list of whom have died more than but I don't go you Delaware where just about their seat alone so each some of the accident is still a long time not that 1 that will in it's been nevertheless a we don't do that so many young woman is not there undergoing a your test system thing has been working I'm with it will at any angle so it's clear that we don't want that there is a friend of both there was no Correa was for operators with you it is possible to there call him all right but there was equals Delaware price a mail what is the right these are raising and lowering the Hamas creation they came in and aluminum along given and they all do what they not we're Mother's Day it is a normal value of LLC will be concentrating on those nothing special about the actors but it would be the vessel wish through the fact to ruin world it uses yet and all a value of asleep who values of our call a 1st age or 8 large number if we say a farmer who won the their life in real time only hours where are backed is just called in that start operation in state Is the angular momentum unit are and can't be quite
call and historical reasons well I have not been brought to elect a lost art that is what but all that they ill where there is as a form of losses would also known as the 2 of us this is a good desire why where by now this is the coming days of those while I might decide what city are more so ls with see you minus and it will work out plus and there for while New York I guess I heard Texas an isolated 1 this is just a a laughter I might your Iowa a combination of my is a watch the but but what about my we have lost when you could give new communities you get back you you go back With designed that he's a member of the next step is 1 of them a scientists are popping up but he will back and let raising like creation and annihilation operators from our house occurs when a health lot we change the key component we also have only made 1 the following year or a lot of money in the form of a mail won 82 of there's not most wickedness when we can 1 direction recalled opposition special policy and it is now possible but e that was possible it will be a man a show that lasts but in increases value so you do that let we have let's call it so that Elzy acting on him this why and in forest that will end in 2 of where I believe that there can act as a I we don't this is what we want rules is that if you will while are present the operator but the it is an object that were not rule is that year With Oregon and what's more With ills you can also so let's not only can do is multiplied by can watch we get really is it is 1 the thing the box we should all get in both and but that is easy computer is lost a community where are what's the point the LC through a new plan your but that we can force held disease ruled last line but it really is a combination of things we can In a loss as much as healthy Of course he will last year it allowed here In the 1st of they it came here was so that 1 side of hostility Ross Taylor loss last year LCO true these last year the man on the left side of of the equation will see it useful so this is a very narrow loss ever acting on a fast but plus upside era questions because we're all but no easy way he can just places Chelsea by him 4 p.m 8 out it wasn't until
the With the new literary boxes of loss of last saying we're not seeing a lot so what's in the box as the quality of the incident if that until but it is I would like to have him boss who lamented letter we have will be given the value sales there must be a last with 1 additional annually they were off by 1 year almost you all that tells elite using alone you could say that my this for gives you an idea that might is now run by the discovered Federer thank you see all his face value but what if but if if it stays like this could be moment is is passed about it it could be might water the we are made as to what is the going to lose a 1 must who would I was always lower in 1 our Yahoo but let pedal on the river will follow the particular part with time we're not talking about in the whole world was is some of the news from community leaders are mostly the seek before it's not the same object before we simply or so but class as wrote about exist and we're not allowed to increase the rate of new but we are not allowed to roam I don't think the angular momentum will increase the without changing the whole but so there's a lot of things it is the give it were given value elsewhere the bank can arise the are was characterized by a man it's also characterized by Lee the angular momentum that square OK so that the is will do more harm than good work and that the maximum annual zinc for flown there are a lot of these massive about the angular momentum on a visit part copper but then we will prove that might be last we're not going to comment on the possibility of stealing the answer is exactly the same harmonic oscillator agrees that there is no no matter what happens the annihilation operators you after that it was it give 0 that's the 1 possibility the last 8 Forest where else will your that can really so all formats there is saying is give object L a loss for all of us called backs so the king of what is the name of God it 1 of the fans the Internet is beat what must be the name Michael that if you could build a system with more taxes so about you must be patient parents reactors being relaxes you must be allowed to have exactly the same value for out there so while trustee of course that you need to be very me and leave us as from next year week a ball hit on their jurors and that then things us on properties use on a recent the located as you know a gap but is only 2 possible think about you only 2 possibilities for they not commit to factories the price of rice 0 is possible value 0 4 and then any was 1 might and so on until you get so they had to get may well on rubber about by the status or those who have heard of that last here last year more that number parcels states that man will give us and that could be depending on the specific part object to talk about so this part of and that in fact call art but there are those this is just 0 and nothing else when you hit the 0 loss to 0 at 0 then there's the possibility of more than 1 is as 1 is still warm it will learn or best thing that has been 1 part last winter they really are exist on Europe he follows are these bows on existing ones are listed as endangered by press time last week
not nearly called element to partner with there are no earlier Best of all was there are galaxies 3 are fine but got lots of objects Israel but among the elements particles because of what they called the fuel want who was not clear if that is possible possibility that In 0 was not expect only other situation where is both and get what they want as the furor over here is a areas of chaos it was my half and then In new 1 so far personal as their sole or to call the way back this all in all I to be an is is all being just as they are called to the warm described far as having been some not only an hour and a half that was adopted with him that's all I have hot metal recalls we are not a part of those companies it is just dream spread the a state and got yet but not the maximum is going to be an the adjourned the 3 maximum 5 fun them all arms you all speculation about an hour or combination Red berries quality can you Have you on our elementary particles in high school that alone 0 0 1 2 0 allowed him so particles of elementary particle 0 1 3 control but you can't do you life will as being wrote to the text where and we can match back fast look I'm I'm a juror who said 1 0 Barcelona was with great I don't that your as of between Bashir we're more about why can't we will not allow please course what room is a must moving an electromagnetic wave of what was yeah meeting circularly polarized waves that's all it fast yeah nevertheless please delete polarized form is 1 with a spin angular momentum along the axis of exact direction a steadily followed ways is composed polarized and circularly polarized means 1 was angular momentum taxes for a long look lot talk about the rest which is autonomy but that doesn't make sense of what promotion head slapping his patient at for the moment the outside Europe who has been I do with Our orientation in relative world Cup returned because it part of it we have In an hour depends on not for we have here is punches it's a matter of speculation as to who Rome conjecture yesterday a super part the rap school grounds he that has ruled text as the whole news yet With but that he also said that the original slug or let them in you will some of them were in it there's not downward I don't lose are we going to do with their dead now we know what you can do not appear to this will using his properties not less than that do we know what it is that release In fact there are number of reasons on the nite of the fire is based not only hinted that 1st of all I the it they basis falsified data is but it is very possible labeled with and but it does not if you laughter that on with so let me down are you throw it and so they have to pay some of squares as you will find that about back the trial would take elsewhere you might think elsewhere in look at this you for the promise with that is that he has no equal and or know people on earth and Max this you 1 he also will tell you that what please or we that's square let computers but was 1 thing which will be yet let's think support elsewhere he what the name History right Of course last nite on so residents were less
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everyone will you could probably know to look and have be hopes that years on your there said not a car who will have to sit on oil as needed to an election on if you it using orbital race use with him yesterday I find need for most of his life each year but I mean what teams have found a solution North creates the and so then how come you have the letter on the thing St there is a principal quantum number these were the most both and your mind From a place called me who you know I'm still young but lacks the means conference pursuant to he has more he is a Mormon ethos and of freedom that's for orbital angular momentum over the other number is this basic distance away from here prime principal so I would not be the actual cost of Castle principal members or call at school they the sale or both principal are rollers following was Norway turned all of our they did that where so said it is showers yet they can knock off this matter your heart here remember do I have to do all the local club for while what that same as your test test 0 that is what little and 0 1 or state the where P is more work but also the only thing in the world was 1 if you are a woman should be weighed beast 5 state sir so we're losing 1 them the them everything everything we express our electrons at all all the things the foreign spurt and then when there's me and there is too much in Riyadh more rounds right exactly the please that and there are some features of the Jolly thinking about what saw rumors OK on question of what it be better says for more
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