- #1

- 14

- 0

## Main Question or Discussion Point

This question was posed to me a while ago, but I never fully understood how to solve it.

You have a particle in the first excited state of the infinite square well (with the origin taken to be at the center. You "abruptly" change the shape of the potential well to be that of the harmonic oscillator and characterize the immediate result on the wave function

Which energy eigenstates of the harmonic oscillator are excited, and how quickly (roughly) must this change be made for it to be considered abrupt?

I think I see that ALL of the odd states of the harmonic oscillator should be excited since you were in an odd state of the infinite well, and I think classifying abrupt has something to do with the energy time uncertainty principle, but I am not sure what value to use for delta-E

Any help is much appreciated

You have a particle in the first excited state of the infinite square well (with the origin taken to be at the center. You "abruptly" change the shape of the potential well to be that of the harmonic oscillator and characterize the immediate result on the wave function

Which energy eigenstates of the harmonic oscillator are excited, and how quickly (roughly) must this change be made for it to be considered abrupt?

I think I see that ALL of the odd states of the harmonic oscillator should be excited since you were in an odd state of the infinite well, and I think classifying abrupt has something to do with the energy time uncertainty principle, but I am not sure what value to use for delta-E

Any help is much appreciated