About expansion of wave functions

[hokhani]

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|?

 

[Simon Bridge]

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.