Lecture 3 | Modern Physics: Quantum Mechanics (Stanford)
March 20, 2011 by Actaphysica
Filed under Physics Videos
Lecture 3 of Leonard Susskind’s Modern Physics course concentrating on Quantum Mechanics. Recorded January 28, 2008 at Stanford University. This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University. Complete playlist for the course: youtube.com Stanford Continuing Studies: continuingstudies.stanford.edu About Leonard Susskind: www.stanford.edu Stanford University channel on YouTube: www.youtube.com
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@supertrunksz YES but remember that the integral is over -∞ to +∞… so the term iΨ*Ψ is evaluated over the same interval (after its implicit integration). This term thus goes to 0 b/c the complete set of eigenstates Ψ form a Cauchy sequence (a req of belonging to a Hilbert space) which implies that at +or- ∞ the eigenstates are 0.
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@amadevs89 No, never in that mathematical method is there any need for the eigenstates (psi function) to be normalized. its straight forward integr’t by parts, which btw is a common method to show operators are hermitian in QM.
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@mdinka eigenfunctions have long been in use to solve many physical problems in nature (not just in QM). they turn out to be fundamenal in linear systems (ie vector spaces) where linear diff equations explain or model the natural phenomana. Asking if there is a deeper meaning to eigen-equations is like asking if there is deeper meaning to why the field of calculus if so important to newtonian mech.
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Isn’t the result of integration by parts as done at (1:30) correct only if the psis are normalized?
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@mdinka As I understand, in general the eigenvectors and eigenvalues are important mathematical objects due to their invariance under (proper) coordinate change. In other words, no matter how you represent a linear operator, it will have the same eigenvectors and eigenvalues, so they are the “essence” of the operator.
You can make an analogy of this to QM, and I think that shows the importance, at least to me.
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is there a deeper sense in why just the features of Eigenvectors and Eigenvalues turn out to be so important for QM?
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When we are finding P(x), shouldn’t we be finding the probability for the particle to be in the interval (a, b) and take the integral from a to b since the function is continuous?
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1:09:01 Obviously Dirac cheated.
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In 1.29.00 shouldn’t we have also another additive, to be precise the iΨ*Ψ ? Because when integrating by parts you have S(f.g’)dx = f.g – S(f’g)dx
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good lecture, but the sound goes out around 1:23:00
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Free lectures on the internet is the best that happened to me in a long time. Thank you Stanford, MIT, Oxford and all the others! Really appreciate it!!
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@reticulum78 thanks a lot…I’ve been reading about it and well, yes, that’s what I’ve learned…in a nutshell:) cheers
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@Sakartvelo69 The dirac delta function operates in a continuous space in much the same way as Kronecker delta does in a discrete space. Any function can be visualized as a continuous sum (integral) of Dirac delta functions where the coefficients are the function values at specific points. X measures the position of a particle so the eigenfunction of this must be localized at one point, and delta(x) is the function that describes this localization.
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brilliant lecture but it still isn’t clear to me how the dirac delta function relates to the psi wavefunction…how does it satisfy the requirement that it is an eigenvector of X? dunno…maybe i’m stupid…i’ll give it some more reading but i think he could have been a bit clearer there…
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