# One dimensional infinite potential well problem

hi,
I am not getting idea to solve below problem
A particle of mass m is in a one-dimensional ,rectangular potential well for which V(x)=0 for 0<x< L and V(x)=infinite elsewhere. The particle is intially prepared in the ground state ψ1 with eigen energy E1. Then , at time t=0, the potential is very rapidly changed so that the original wave function remains the same but V(x)=0 for 0<x<2L and V(x)=infinite elsewhere.Find the probability that the particle is in the first,second,third and fourth excited state of the system when t ≥ 0.

Dick
Homework Helper
When the potential is changed suddenly the original wavefunction stays the same. To compute the amplitudes of being in any other state then just compute the overlap integral <psi1|phi> where phi is the wavefunction of the excited state. To get the probability find the modulus squared of the amplitude.

When the potential is changed suddenly the original wavefunction stays the same. To compute the amplitudes of being in any other state then just compute the overlap integral <psi1|phi> where phi is the wavefunction of the excited state. To get the probability find the modulus squared of the amplitude.

the |phi> is the excited states in the new potential, right??

Dick
Homework Helper
the |phi> is the excited states in the new potential, right??

Sure.

compute the overlap integral <psi1|phi> where phi is the wavefunction of the excited state.
Two quick questions:

1. Is this 'overlap integral' the convolution of the wavefunctions in each potential?

2. Is taking this 'overlap integral' in such a situation generally the way to tackle problems such as this?

Dick