About expansion of wave functions

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SUMMARY

The discussion centers on the expansion of a particle's ground state wave function when transitioning from a one-dimensional box of length 'a' to a larger box of length '10a'. It is established that the initial expansion of the wave function in the region x > |a| is zero, as the particle is initially confined to the interval 0 < x < a. Upon changing the box width, the probability of finding the particle in the region a < x < 10a remains zero at the moment of transition. Over time, the wave function will expand to occupy the entire new box, demonstrating dynamic behavior.

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hokhani
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Suppose in one dimension we have a particle in box with the length a. If we were to expand it's ground state wave function in terms of the state functions of the particle in another box (with the length for example 10a), is the expand automatically zero in the region x>|a|?
 
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If, initially, you have a particle confines to 0<x<a, then it is confined to 0<x<10a, then the initial probability of finding the particle in the region a<x<10a must also be zero at the instant of the change in box-width. That would be a yes. With time, the wavefunction will expand into the rest of the new box and generally slosh about.

Note: by the same description you could have gone from -a/2 < x < a/2 to -5a < x < 5a. This will make a difference to the expansion.
 

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