Consider the harmonic oscillator with a Gaussian perturbation p² 1 H 2μ + z μw ²x² +Ve-αx² Show that the first-order correction term to the ground state energy is 1/2 μω/h v\a+μw/h/ Hint: Ground state wavefunction 4 μω πh Po(x): = · e-μwx²/2ħ

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