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A particle of mass m and electric charges q can move only in one dimension and is subject to a harmonic force and a homogeneous electrostatic field. The Hamiltonian operator for the system is

H= p^{2}/2m +mw^{2}/2*x^{2}- qεx

a. solve the energy eigenvalue problem

b. if the system is initially in the ground state of the unperturbed harmonic oscillator, ket= |0>, what is the probability of finding it in the ground state of the full Hamiltonian?

Could any body offer some methods to handle this question? Thank you very much.

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# A question about solving the energy eigenvalue of a given Hamiltonian operator

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