What Happens to a Particle's Energy When a 1D Box Shrinks?

[msumm]

what happens if we have a particle in a 1D box at the lowest energy level, and we shrink the box? i realize that it would need to get go to a higher energy level to continue to satisfy Schrödinger's eqn in the smaller box. is that what happens? any links or explanation of the process?

thanks

 

[f95toli]

No, the particle stays put. The energy levels shift.

What you are describing happens in e.g. a Josephson junction when you change the bias current (the shape and depth of the junction potential depends on the current); this effect can be seen quite easily macrosopic quantum tunneling (MQT) experiment and/or resonant activation.

Note that this assumes that you are changing the shape adiabatically. If you somehow change the shape very quickly things change and you might even be able to induce Landau-Zener transitions.