1 Introduction 2 Resolvents and Green's Functions

(b) From your answer to part (a), show that, for α = 2:
φ(x; t) = ( mω
π ) 1 4 exp
{
− mω
2 (x − a cos ωt)2 − iω 2
You should give some thought to how you might have attacked this
problem using “elementary methods”, without knowing U(x, y; t).
(c) Notice that the choice α = 2 corresponds to an initial state wave
function something like a “displaced” ground state wave function.
Solve for the probability distribution to find the particle at x as
a function of time (for α = 2). Your result should have a simple
form and should have an obvious classical correspondence.
[
t + 2max sin ωt − m a2
2 sin 2ωt ]}
.
(131)
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