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 Apr 15 accepted How do I correctly interpret $\rho = \psi_1^* \psi_2$? Apr 14 comment What is the difference between $|0\rangle$ and $0$? wow! I see. thanks! Apr 14 asked How do I correctly interpret $\rho = \psi_1^* \psi_2$? Apr 14 comment What is the difference between $|0\rangle$ and $0$? @Tedd Bunn one question: can't we have a state $|0\rangle$ where the ket represents a column vector in a particular basis where all components are zero? for an analogy in 3-space.. take a point with finite coordinates and shift the origin to that point, and in this new basis the point is represented as a 0-component vector. Apr 12 comment Who works professionally on reformulation of QFT? I think the upvotes to this answer serve a very bad example. (even though they're probably motivated by a notorious history of the OP) Apr 9 comment Correspondence principle @Noldorin I think you mean $-\frac{i}{\hbar}$ times the commutator 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? added 392 characters in body 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