Properties of derivatives of a wavefunction?

[Torboll1]

Hi!

I'm currently re-reading Griffiths introductory QM book and plan to do most of the exercises. I got stuck on one problem and had to look for some hints and found two solutions that both claim that:

$$\int_{-\infty} ^{\infty} \frac{\partial }{\partial x}\left[ \frac{\partial \Psi ^{*}}{\partial x} \frac{\partial \Psi}{\partial x} - \Psi ^{*} \frac{\partial ^2 \Psi }{\partial x^2} \right] dx = 0 .$$

What Griffiths really push is that the wave function approaches zero at the boundaries but he states nothing about the derivatives (other than that they need be continuous). Can someone help me understand this?

 

[soothsayer]

The derivative of a wavefunction out to infinity should approach zero as well. This is the same as in, say, an infinite well, where the wavefunction must be zero at the well wall. For the derivative of the wavefunction to also be continuous at the boundary, it must approach zero smoothly.