Is it always true that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d\psi}{dx} \rightarrow 0[/tex]

(at ±infinity)? And if so, why?

I know that for a wave function to be normalizable, we must have psi-->0 at ±infinity but as far as i can see, that does not imply that the derivative will be 0. A counter-exemple of this is a decreasing "sine-like" function with an oscillation frequency inversely proportional to its amplitude. For instance

[tex]\psi(x) = A(x)sin(x/A(x))[/tex]

for x>=0, and

[tex]\psi(x) = \psi(-x)[/tex]

for x<0., with

[tex]A(x) = e^{-x}[/tex]

This function goes to zero at ±infinity but it's derivative is wild at ±infinity.

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# Homework Help: Another QM detail

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