# Perturbation Theory (Non-Degenerate)

by jhosamelly
Tags: nondegenerate, perturbation, theory
 P: 126 If I have V(x)=$\frac{1}{2}$m$\omega^{2}$x$^{2}$ (1+ $\frac{x^{2}}{L^{2}}$) How do I start to solve for the hamiltonian Ho, the ground state wave function ?? Calculate for the energy of the quantum ground state using first order perturbation theory?
 P: 1 $H= H_{0} + H_{p}$ So basically, you have an aditional term, $H_{p} = \frac{1}{2L^{2}}mω^2 x^4$, that perturbates your hamiltonian. You already know the solution for the harmonic oscillator, $H= H_{0} = \hbarω(n + \frac{1}{2})$, so you just have to find the corrections for the $H_{p}$. hope i made myself clear ( ;
 P: 126 so does this mean my hamiltonian would be $H= \hbarω(n + \frac{1}{2}) + \frac{1}{2L^{2}}mω^2 x^4$ ?