Let us consider a shifted harmonic oscillator, given by the Hamiltonian Hˆ = pˆ ^2/2m + 1/2 mω2xˆ 2 + cxˆ,
where c is a real constant.
(a) Compute the eigenvalues and eigenfunctions of this Hamiltonian as functions of c.
(b) For the ground state, compute the expectation values <xˆ> and <pˆ> as functions of c.
(c) What is the physical meaning of the constant c?