Using TIPT on a quantum harmonic oscillator:

tex2html_wrap172 with perturbation, tex2html_wrap173

Exact solution: tex2html_wrap174 , so tex2html_wrap175 , whiych is just the standard solution displaced a little. Solution: tex2html_wrap176 and tex2html_wrap177 . Then tex2html_wrap178 , which gives the solutions tex2html_wrap179 with eigenstates tex2html_wrap180 and tex2html_wrap181 where tex2html_wrap182 is the nth hermite polynomial.

Using perturbation theory, tex2html_wrap183

tex2html_wrap184 , tex2html_wrap185 tex2html_wrap186 = exact solution.

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