I had a course of computational physics in university. When the professor wanted to non-dimensiolize the Schrodinger equation, among other things, he changed the wave function using the relation [itex] |\psi(x)|^2 dx=|\phi(y)|^2 dy [/itex] where y is the non-dimensionalized postion ([itex]y=\frac x a[/itex]) and so [itex] \phi(y)=\frac{1}{\sqrt{a}} \psi(x) [/itex]. This seems reasonable to me because wave function has dimension of [itex] [L]^{-\frac 1 2} [/itex] in one dimension. But when I search the internet for non-dimensionalization of Schrodinger equation, non of them do this step. Why? What's the point?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks

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# Non-dimensionalization of Schrodinger equation

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