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Ψ(x,t)=Ae^-a(mx^2/η+it)

A particle of mass m is in the infinite, one-dimensional, time-dependent state:

where A and a are positive real constants. What are: (a) normalization constant A, (b) the potential energy function, U(x), which satisfies Schrödinger equation with (x,t) being its eigenfunction, (c) the quantum-mechanical expectation value of x, (d) the quantum-mechanical expectation value of x2, (e) the quantum-mechanical expectation value of momentum ^p, and (f) the quantum-mechanical expectation value ^p2