Sudden changes, what happens to particle?

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SUMMARY

The discussion focuses on the behavior of a particle's wavefunction when the confining box undergoes sudden expansion from 0 to A and then to 0 to 2A. In cases of rapid expansion, the wavefunction remains unchanged initially and subsequently diffuses according to the Schrödinger equation, resulting in a departure from the ground state. Conversely, during slow or adiabatic expansion, the wavefunction remains in the ground state of the new box configuration throughout the process.

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Let's say we have the typical ground state particle in a box. The box suddenly expands from 0 to A, to 0 to 2A.

What happens to the wavefunction of the particle?
 
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If the expansion is extremely fast, then the wave function remains the same as it was before and then slowly diffuses out according to the Schroedinger equation (it will no longer be in the ground state).

If the expansion is slow (also called adiabatic) then the wave function remains in the ground state of the "new" box at each step in time, and ends up in the ground state.
 
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