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(2) Consider a particle in 1D subject to a harmonic potential energy. The center of the potential is shifted
compared to the usual form. The Hamiltonian is given as H = P+^
+(f-a)'. Based on physical reasoning,
2m 2
determine the energy spectrum and write down the energy eigenfunctions without doing difficult math just
by matching to known results for the case that a = 0. Mathematically justify your results.

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