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How how can we calculate the future evolution of a particle after the infinite square well potential is (somehow) turned off, releasing it into a free state? Assuming that it was in the ground state before.
After turning off the potential, the wave function will evolve as a superposition of plane waves.Apart from brute force / numerical, is there a nice way to solve this (or to get useful qualitative properties of the solution)? For example, in the absence of ##V(x)##, can we transform the ##\psi(x,t=0)## into ##\psi_p(p,t=0)## and find the future ##\psi_p## in a simple way?