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1. The problem statement, all variables and given/known data

An additional term V_{0}e^{-ax2}is added to the potential of the simple harmonic oscillator (V and a are constants, V is small, a>0). Calculate the first-order correction of the ground state. How does the correction change when a gets bigger?

2. Relevant equations

[tex]E_0^1=<\psi_0^0|H'|\psi_0^0>[/tex]

3. The attempt at a solution

[tex]\alpha=\frac{m\omega}{\hbar}, E_0^1=\int ^{\infty}_{-\infty} (\frac{\alpha}{\pi})^{1/4}e^{-\alpha x^2/2}V_0e^{-ax^2}(\frac{\alpha}{\pi})^{1/4}e^{-\alpha x^2/2}dx=(\frac{\alpha}{\pi})^{1/2}V_0\int ^{\infty}_{-\infty} e^{(-\alpha -a)x^2}dx[/tex]

So I suppose this is not what is wanted.

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# Perturbation of the simple harmonic oscillator

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