(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a particle in a one-dimensional box whose (time-independent) state is given by

e^ikx. Of course, this corresponds to the particle moving with a momentum of magnitude hk in the positive (let's call it x) direction.

I know momentum in the quantum sense cannot be regarded as momentum in the classical sense. I am struggling to conceive how a particle in such a bounded system can always have momentum in one direction- how can it renew itself when it reaches the right boundary? I am thinking it has something to do with (complex) traveling waves, but i can't put my finger on it. I also looked in a few books on quantum mechanics and was able to find the following lines, which I believe applies to my inquiry somehow:

"In a nutshell: the formal problem with applying the classical definition of momentum to an ensemble of microscopic particles arises becauseit is impossible to measure the position of such particles without altering their state. This vicissitude is inevitable, because prior to measurement, the particles do not have a position or a momentum."

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# Momentum for a particle

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