Consider a one-dimensional harmonic oscillator perturbed by a linear potential, (lambda hat{H}_{1}=lambda x). Calculate the first-order perturbation
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Consider a one-dimensional harmonic oscillator perturbed by a linear potential, \(\lambda \hat{H}_{1}=\lambda x\). Calculate the first-order perturbation theory corrections to the energy and wave functions, and compare with the exact solution for \(\hat{H}_{0}+\lambda \hat{H}_{1}\) (which is trivial to find in this case).
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