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I am reading something on wave function in quantum mechanics. I am thinking a situation if we have particles distributed over a periodic potential such that the wave function is periodic as well. For example, it could be a superposition of a series of equal-amplitude plane waves with different wave number (some positive and some negative) so to give a form of ##f(x+2\pi)=f(x)##. In this case, I wonder how do we normalize the wave function. I try the following but it almost give something close to zero because the integral gives something very large

##

f [\int_{-\infty}^{+\infty}|f|^2dx]^{-1}

##

But since it is periodic, do you think I should normalize the wave function with the normalization factor computed in one period as follows:

##

\int_{-\pi}^{+\pi}|f|^2dx

##

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# I About normalization of periodic wave function

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