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seen Oct 6 '14 at 12:28

Learning from scratch


Apr
8
awarded  Suffrage
Apr
7
comment Why is the Earth so fat?
@Luboš Motl on an unrelated note mnnttl.blogspot.com/2011/02/latex-on-blogger.html for using stackexchange style latex in blogspot
Apr
6
comment About the complex nature of the wave function?
the uncertainty relations follow from the identification of the free particle as a plane wave. I am guessing your answer points in the right direction, I am working on (2) as suggested in Lubos' answer as well and trying to get why $\psi$ is complex valued as a consequence, however I fail to see how anything except (2) is relevant for showing it conclusively.
Apr
6
comment About the complex nature of the wave function?
Please clear some doubts for me. 1. The probability interpretation: I think it followed since the wavefunction was complex and physical meaning could only attributed to a real value. If we make a construction $\psi^*\psi$ then we arrive at the continuity equation from the schrodinger equation and the interpretation can now be made that the quantity $\rho=\psi^*\psi$ is the probability density. Starting from an interpretation like $\rho=\psi^*\psi$, I do not see any way to work backwards and convincingly argue that the amplitude $\psi$ must be complex.
Apr
6
comment Phase shifts in scattering theory
upvoting your question as I think a good explanation for partial waves will be good for the site.. you may wish to change your question slightly perhaps to get new answers though
Apr
6
awarded  Quorum
Apr
6
comment About the complex nature of the wave function?
@Carl Brannen my question is introductory and pertains to the non-relativistic schrodinger equation for one spinless particle. is it relevant in that context.
Apr
6
awarded  Commentator
Apr
6
comment About the complex nature of the wave function?
@Carl Brannen Do you upvote an answer just because it cites the work of someone you respect, despite the fact that it might be of little relevance to the question?
Apr
6
comment About the complex nature of the wave function?
@Helder Velez I am one of your downvoters as I saw it as a very broad answer with lots of references and abstracts reproduced which have little to do with the specific context in which I tried to frame my question. Also, I am not interested in the interpretational aspect of Quantum Mechanics at all, at my stage.
Apr
6
revised About the complex nature of the wave function?
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Apr
6
comment Phase shifts in scattering theory
Also, I don't think that Sakurai is a good way to learn these topics if you are learning about them for the first time. Try the more accessible texts first. I would recommend Shankar\Griffiths.
Apr
6
comment Phase shifts in scattering theory
What do you need to know? Its used in partial wave analysis, a common orthogonal expansion . Any function can be decomposed into infinitely many partial waves, the different partial waves correspond to different angular momenta physically. The phase shifts come up as one of the constants that need to determined from the boundary conditions for each partial wave. The scattering amplitude can be expanded in terms of the phase shifts of the waves and spehrical harmonics. I am not writing this as an answer and cluttering it with equations because its there in all standard texts. Eg.-Griffiths etc
Apr
6
revised About the complex nature of the wave function?
edited title
Apr
5
comment How to explain independence of momentum and energy conservation in elementary terms?
@englishphysics KE is conserved in a way but not in the system that the problem focuses on. If you look at just the system of the two balls, it is not conserved. However the whole balls colliding thing is an open system which can exchange energy with its environment so the KE of the balls will be transferred as KE in the faster jiggling of nearby air molecules,as heat.. if you think that is too obtuse or confusing for a 16 year old then you're really underestimating them.
Apr
5
revised About the complex nature of the wave function?
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Apr
5
comment About the complex nature of the wave function?
I edited my question removing the reprints and trying to state my problem without them.. it will take some time to think about some points you made in the answer already, though.
Apr
5
revised About the complex nature of the wave function?
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Apr
5
comment About the complex nature of the wave function?
thanks for answering. I have one question, not knowing about Feynman path integrals yet, I take it that what you are saying is the same thing as: if we make the transformation $\psi(r,t) = e^{i\frac{S(r,t)}{\hbar}}$ then the Schrodinger equation reduces to the classical hamilton Jacobi equations (if terms containing $i$ and $\hbar$ were negligible)?
Apr
5
revised About the complex nature of the wave function?
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