Question

A one-dimensional simple harmonic oscillator is subjected to a small perturbing potential W(x), producing a simple at the center of the motion. Thus

Calculate the correction to the ground state energy of the oscillator to first order in λ in the event that

(a) \(\alpha <<\sqrt{h/m\omega}\)

(b) \(\alpha >>\sqrt{h/m\omega}\)

Hints: the normalized ground state wave function of a simple harmonic oscillator is

Answer 1

The energy correction for the ground state given by first order perturbation is