A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is 1/6 gamma x3 ( gamma is a constant). Using only the first order correction, the total ground state energy of the anharmonic oscillator is Note: For aone-dimensional harmonic oscillator 0(x)= (( alpha )/( pi ) )1 / 4 e^- alpha x2 ; alpha = (k mu h2 )1.2

ABC26PH0324 · Atomic Structure

Subject: Physical Chemistry · Chapter: Atomic Structure · Topic: Atomic Structure – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is $\frac{1}{6} \gamma \mathrm{x}^{3}$ ( $\gamma$ is a constant). Using only the first order correction, the total ground state energy of the anharmonic oscillator is Note: For aone-dimensional harmonic oscillator $\psi_{0}(\mathrm{x})=\left(\frac{\alpha}{\pi}\right)^{1 / 4} \mathrm{e}^{-\alpha \mathrm{x}^{2}} ; \alpha=\left(\frac{\mathrm{k} \mu}{\mathrm{h}^{2}}\right)^{1.2}$

(a)$\frac{1}{2} \hbar\left(\frac{\mathrm{k}}{\mu}\right)^{1 / 2}$

(b)$\left(\frac{1}{2}+\frac{\gamma}{6}\right) \hbar\left(\frac{\mathrm{k}}{\mu}\right)^{1 / 2}$

(c)$\left(\frac{1}{2}+\frac{\gamma}{3}\right) \hbar\left(\frac{\mathrm{k}}{\mu}\right)^{1 / 2}$

(d)$\left(\frac{1}{2}+\frac{\gamma}{12}\right) \hbar\left(\frac{\mathrm{k}}{\mu}\right)^{1 / 2}$

Answer

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Explanation

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