Calculating Transition Probability for Particle Mass "m

[amarante]

I need some help how can I calculate a transition probability on this problem: A particle of mass "m" on a potential well (1), where it V(x) is infinite for x>L/2 and for x<L/2 . Inside the region V(x)=0 . I know how I get the eigenfunctions and the Energy.
But, than the potential (2) well expands instantly and now it is infinite for x>L and x<L . and it is zero inside that region.

I have to calculate the probability that the particle on the ground state for the potential 1 will go to the first excited state on the potential 2.

Should I use pertubation theory and consider this expansion of the potential as a pertubation? And if yes, how do I write this pertubation?

Thanks in advance

 

[George Jones]

I need some help how can I calculate a transition probability on this problem: A particle of mass "m" on a potential well (1), where it V(x) is infinite for x>L/2 and for x<L/2 . Inside the region V(x)=0 . I know how I get the eigenfunctions and the Energy.
But, than the potential (2) well expands instantly and now it is infinite for x>L and x<L . and it is zero inside that region.

I have to calculate the probability that the particle on the ground state for the potential 1 will go to the first excited state on the potential 2.

Should I use pertubation theory and consider this expansion of the potential as a pertubation? And if yes, how do I write this pertubation?

Thanks in advance

I think that you're making the question harder than it actually is.

Immediately after the expansion, the wave function of the system is still the ground state wave function for the narrow well. What is the wave function for the first excited state of system immediately after the expansion?

Use these two wave functions to calculate the transition probability.

 

[cartonn30gel]

I recall a very similar problem from Griffiths' QM. You might want to take a look.