How to solve an anharmonic oscillator perturbation problem?

[leright]

I have a homework problem that is kinda driving me nuts...

Consider the case of an anharmonic oscillator with microsystem quantum states given by Ej = jhf - (lambda)(jhf)^2.

Using the known harmonic expressions as a starting point, determine the corresponding expression for F1 and for F, which is about equal to Fo + (lambda)F1.

Can someone give me a hint on how to approach this problem? I figure I could find the partition function easily enough since Zj = sum(e^(-(beta)Ej)). I can then plug in Ej into the Zj function. However, I am not sure how to determine that sum. Am I even approaching this problem in the right way?

Thanks.

 

[dextercioby]

IF you have the partition function, how do you get the F ?

Daniel.

 

[marcusl]

Hi leright,
This
looks like a perturbation problem to me. You don't need the perturbing potential V1 since you have the eigenvalue given in the form of an unperturbed part (relate that to the unperturbed H.O.) and a perturbation of strength lambda.