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I have just started an introductory course on quantum mechanics, and there are some things that I can't figure out. Similar questions have probably been answered several times before, so links to other threads are very welcome (I can't seem to find them using the search-function, I'm sorry).

Here goes:

My textbook starts out by stating that all matter posess both particle- and wave-properties. It introduces something called the "de Broglie wavelength" for particles, which is [tex] \lambda = h/p = h/mv [/tex].

Later on, it introduces "wave functions" for particles (denoted [tex] \psi(x,y,z) [/tex] or [tex] \Psi(x,y,z,t) [/tex]) which must satisfy Schrödingers equation. As I understand, the (complex) wave function, in itself, has no physical meaning, but [tex] |\psi(x,y,z)|^2 [/tex] is somehow (?) related to the probability of finding the particle near (x,y,z).

My questions here are:

1) What is the relation between the de Broglie wavelength for a particle and the wave function for that particle? If the wave function has no physical counterpart, then what is the wavelength? In classical physics the wavelength is the distance between two points of a wave that are in the same "state" - is that also the case with the de Broglie wavelength? If so, what does this "state" refer to (in sound waves it is related to pressure, in em-waves it is related to the E- and B-fields etc.)? Bottomline: In what sense are particles waves?

2) [tex] |\psi(x)|^2dx [/tex] (we are working in 1-d here) is said to be (proportional to?) the probability of finding a particle in an interval dx around x. But this probability must depend on how long you are looking at this interval, so what exactly is meant by this?

3) Like I mentioned above, my book talks about two wave functions - a time-dependent [tex] \Psi(x,y,z,t) [/tex] and a time-independent [tex] \psi(x,y,z) [/tex]. Even though there is a time-dependence they also consider (and use) the time-independent version. What meaning does this have in a situation where thereistime-dependence?

I have several other questions, but these are the main ones I guess (besides the ones I forgot).

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# Basic QM questions

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