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An electron is confined by the potential of a linear harmonic oscillator V(x)=1/2kx^{2}and subjected to a constant electric field E, parallel to the x-axis.

a) Determine the variation in the electron’s energy levels caused by the electric field E.

b) Show that the second order perturbation theory gives the exact value to the same variation.

c) The system’s electric dipole moment in the n-th state is defined by p_{n}=-e<x>_{n}. What is the electric dipole moment for the electron in the harmonic oscillator’s potential, in the absence and in the presence of the electric field E?

Thanks in advance!

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# Perturbation theory / harmonic oscillator

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