I was thinking about the "distribution" of a particle in space in different situations. An electron bound in a atom have a wave function that is broad.(adsbygoogle = window.adsbygoogle || []).push({});

What about the broadness of the wave function of conduction electrons in a wire? Or doesn't it even make sense to quantum-mechanicaly speak of conduction electrons in a wire?

What about the broadness of the wave function of a free electron? By free I mean an electron that is not interacting with any nearby particles or "classical" fields. (I know that just saying nearby is vague (How nearby?), but I hope you understand what I mean.)

So I was trying to answer myself the two questions above, and I started by thinking this way:

The time evolution of a wave function is governed by the hamiltonian of the system and I guess the hamiltonian is non-zero only if the system has energy. So in both cases above, I would expect the wave function to be changing in time.

Also, the broader the wave function, the narrower the momentum function -which measures the distribution of momentum through space-. In the case of the electrons in a wire, I guess they are constantly being atracted by the other charges that form the atoms and by the other electrons as well, but I don't have an idea of how fast they move (in average, at least). For a free electron, it would be easy to conclude that how fast the electron is moving will dictate how broader is its wave function.

I used the term wave function to mean position function, actually.

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# B "Distribution" of a particle in different situations

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