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Question Number 199705 by jlewis last updated on 11/Nov/23

$$\mathrm{Calculate}\mathrm{the}\mathrm{first}\mathrm{order}\mathrm{energy}\mathrm{correction}$$$$\mathrm{for}\mathrm{the}\mathrm{one}\mathrm{dimentional}\mathrm{non}-\mathrm{degenerate}$$$$\mathrm{an}\mathrm{harmonic}\mathrm{oscillator}\mathrm{whose}\mathrm{harmiltonian}$$$$\mathrm{id}\mathrm{written}\mathrm{as};$$$$\hat{\mathrm{H}}=-\frac{{\mathrm{h}}^2}{2m}\frac{{\mathrm{d}}^2}{{\mathrm{dx}}^2}+\frac{1}{2}{\mathrm{kx}}^2+\frac{1}{5}\mathrm{{\rm Y}}{\mathrm{x}}^3+\frac{1}{12}\beta {\mathrm{x}}^4$$

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