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I've been scouring through many text books to try find some kind of solution to a question I have been asked for a problem sheet and was wondering if any1 would be able to help. The question is as follows;

The simple harmonic oscillator with hamiltonian H = (p^2/2m) + (1/2(mw^2x^2) is modified by adding a small extra potential V(x) = (1/2(ma^2x^2)). Use the first order perturbation theory to calculate the change in the ground state energy. How does this estimate differ from the exact result?

Unfortunately, I don't think we've covered it clearly enough in our lectures and I cant quite find anything specific enough in text books to answer it, so any help would be much appreciated.

Cheers

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# Homework Help: Adding a small extra potential to a simple harmonic oscillator

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