Chapter 12, Problem 12.34E

An anharmonic oscillator has the potential function

$V=\frac{1}{2}k{\text{x}}^2+c{\text{x}}^4$

where $c$ can be considered a sort of anharmonicity constant. Determine the energy correction to the ground state of the anharmonic oscillator in terms of $c$, assuming that $\hat{H}°$ is the ideal harmonic oscillator Hamiltonian operator. Use the integral table in Appendix $1$ in this book.