Problem 1. Consider a particle of mass m in 1D described by the Hamiltonian Н + a(pr + xp) + Br? 2m where a and 3 are re

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Problem 1. Consider a particle of mass m in 1D described by the Hamiltonian Н + a(pr + xp) + Br? 2m where a and 3 are real constants, p is the momentum, and r is the coordinate of the particle. (a) For what values of a and 3 this Hamiltonian is bound from below? (To clarify: the expression operator is bound from below" means that all eigenvalues of the operator lie above a certain (lowest) value). (b) Find the eigenvalues of H.