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Physics, 12.01.2021 18:00 1109pacey

Consider a charged particle in the one dimensional harmonic oscillator potential. suppose we turn on a weak electric field. Suppose we turn on a weak electric field (E), so that the potential energy is shifted by an amount H= -qEx. a. Show that there is no first-order change in the energy levels, and calculate the second-order correction.
b. The Schrodinger equation can be solved directly in this case, by a change of variables: x' = x - (qE/mw2). Find the exact energies, and show that they are consistent with the perturbation theory approximation.

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