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I have to find the complete energy eigenvalue spectrum of a hamiltonean of the form:

H = H0 + c

and also another of the form

H = H0 + [tex]\lambda[/tex]x[tex]^{2}[/tex]

Where in both cases, H0 is the hamiltonean of an harmonic oscilator, c and lambda are constants. The variable is x.

I have to find the exact eigenvalues, cannot use perturbation theory, but I can use the fact that I already know the eigenvalues for the harmonic oscilator.

Can anybody help?

Thant you.