- #1
KFC
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Hi all,
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
##
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
##