ฝัง
- เผยแพร่เมื่อ 27 ก.ย. 2024
- (November 13, 2009) Leonard Susskind discusses the theory and mathematics of angular momentum.
Leonard Susskind, Felix Bloch Professor of Physics, received a PhD from Cornell University and has taught at Stanford since 1979. He has won both the Pregel Award from the New York Academy of Science and the J.J. Sakurai Prize in theoretical particle physics. He is also a member of the National Academy of Sciences.
Stanford University:
www.stanford.edu/
Stanford Continuing Studies Program
csp.stanford.edu/
@chloeagnew1 The mathematical difference is that the orbital angular momentum is (classically) the motion of the center of mass of the system with respect to a fixed axis. In classical systems of discrete particles, the spin angular momentum of the system is the vector sum of the angular momenta of the constituent particles (usually with respect to an axis that passes through the object, and specifically one that passes through the moment of inertia)...
I am fed up with some of the questions in the lectures, they interrupt the flow of the lessons, here are the timestamps of the question. Note, (x) indicates the less important, less interesting question. (o) indicates somewhat important questions he addresses in more detail, (these indicators are completely arbitrary, skip at your own ‘risk’)
12:24 - 15:21 (x)
1:04:37 - 1:09:32 (x)
1:17:40 - 1:18:13 (x)
1:37:54 - 1:42:58 (x)
Prof. Susskind is such a good sport.
Love you sir susskind....!👍👍👍👍👍👍👍👍👍
Ever wondered why an electron has only a definite value of the spin? Prof. Susskind's got the answer! :)
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍👍
good teacher
good job he didn't pick a and p !
Things mix with space while creating and separate while anhillation like steady and pulsating universe or all things in universe
He finds the spin commutator relations using 'angular momentum operators' which he builds from classical angular momentum and the operator definitions of position and momentum. Do these operators have eigenstates in the space of 'ordinary' wavefunctions (normalised L^2 integrable maps R(3,1)-> C ? If so, what's with everyone using the vector representation? Surely, then, the use of that representation would be redundant....
its a-ness and b-ness of the system. referring to the a and b properties of the system
...for a solid object, it would be the integral of the angular momentum of the individual differential mass elements over the object. Quantum particles, however, have a spin angular momentum due to the "intrinsic spin" of the particle. It's a quantity that has no equivalent conceptualization in classical physics. Whereas the spin angular momentum for a classical system can be described as Iw (moment of inertia times angular velocity), this equation breaks down when talking about point particles.
If a system of two electrons makes a boson, then how come, even though two individual electrons of the same spin cannot inhabit the same orbital, why couldn't multiple coupled systems of two electrons (a singlet) inhabit the same orbital. Electron singlets would be spin 0 (+1/2 - 1/2). Therefore, should they not be able to behave as bosons and coexist in the same orbital?
Frequency density-intensity alignment and geometrical partioning Scattering angles are directly related in superposition to coherence-cohesion e-Pi-i sync-duration resonance bonding and vanishing-into-no-thing perspective-drawing objectives.
Holographic Principle Imagery projection-drawing Actuality..
"Interleaving" is the wave-packaging of "Cofactor Conduction" prime-connection of ONE-INFINITY, = superposition, Polar-Cartesian coordination, Hydrogen-Atomic instantaneous Form.
The concept of pumping a Laser applies generally as e-Pi-i sync-duration connectivity, Reciproction-recirculation.., Vertices in vortices=> specific Feynman type guessing diagrams of disintegration and reintegration, in Perspective. (Only a movie picture sequencing can make simplified sense of conic-cyclonic coherence-cohesion complexity, or familiarity with WYSIWYG cause-effect, Actual Intelligence)
Even if you had told me that particles are node-antinode foci of self-defining time-timing sync-duration substantiation, the cause-effect of transverse trancendental e-Pi wave-particle condensation-interference.., something I've been vaguely aware of because of the ubiquity of AM-FM Communication In-form-ation, yes it's self-defining but the obviousness of WYSIWYG QM-TIME resonance floating Singularity-point positioning Conception is "too simple".
We're evolved to analyze and breakdown encountered Actuality in the purest Reductionist Observation process available, learning by doing experience, and guessing good and bad, right or wrong, etc and eventually deciding what is what, how it be-came and why it should be-cause-effect, ..correctly identifying and making substantiation decisions in a metastable continuous context, ie is what you think you see a possibly in a particular quantifiable balanced equilibria, that has been discounted as steady-state because the real-time Actuality, frozen state of Zero Kelvin flat-space ground-state, No-thing-defined as different eternally, is imperturbable at the limit of "steady". No-thing is what you think you understand in material abstraction?, it's all chemistry and resonance bonding in QM-TIMESPACE Perspective.
1:38:35 - that seems like a reasonable way to use the word orbital.
@technopagan724
Two electrons with opposite spin do not make a boson, but a superposition of two electrons,total spin 0. From a reasonable distance, this can be approximated by a single particle with spin 0, i.e. a boson: the unc. princ.: ΔxΔv = hbar/2m so if the mass is very large, then it's a good approximation (pi meson) if you don't localize the particle so that the speed of its parts takes it far of the localization. Electrons around the atom OTOH do see the separate parts.
@1:24:35 What means of the "combination the overall phase bring down to only 2 variables"?
maybe it's late for you, but someone else might benefit:
if you have a |+> + b|->, you can just multiply this state by b*/|b| without changing the state, since this number is just a change in phase.
So in the end, you can always have a|+> + b |->, where a is a complex number and b is a real number. So you're left with 3 actual variables.
Add to that the constraint of Re(a)^2+Im(a)^2 + b^2 = 1 and you are limited to only 2 free variables, because any two determine the third one.
For example, you can write a = sqrt(1-b^2) (cos(t) + i sin(t)). So the only two variables you need are t and b, which are two real numbers.
The Uncertainty Principle: delta x delta p is greater than or equal to ... whatever ... er.... 29:30
Walker Helen Clark Elizabeth Garcia Timothy
“I have a date with my pillow”
Ugh - bad audio around half an hour in.
If QM is ultimately the correct description of physical reality, then this idea applied to the so-called holographic principle (which depends deeply on waves, not particles) implies that this universe is a sophisticated digital hologram.
21:57 says the man who cant keep track of signs
this time white board is not seeable.
Electron singlets would be spin 0 (+1/2 - 1/2)
Contemplating the relativity of Physics and Chemistry, I would personally prefer
Physics.
Brian Estremos chemistry is physics of matter
❤Thank you very much Professor and class.
interesting TNX