One of the problems in QM i frequently encounter in all textbooks is the shifting of the wall problem which goes like this.(adsbygoogle = window.adsbygoogle || []).push({});

Assume a particle is in the ground state (or any stationary state) of an infinite potential well between 0<x<a. If the wall at a is suddenly shifted to 2a, then what is the probability of finding the particle in the ground state (or any other stationary state) of the new well.

The way I understood it, the solution involves the assumption that since the wall is shifted suddenly, the wave function does not change. However, since the system itself has changed, the new system has different stationary states. The original wave f is a linear combo of these eigenstates and the probability of finding it in one of these states is the corresponding coefficient mod-squared.

My question is since the wave function is unchanged, it looks like

ψ= sin(∏x/a), 0<x<a

ψ= 0 elsewhere

Then at x=a, dψ/dx is discontinuous, even though V≠∞.

How is such a wave function allowed?

Or is my understanding of the solution to the problem wrong?

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# Shifting of the wall problem

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