Coherent state problem in quantum mechanics

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Homework Statement


Typed problem text on quantum mechanics: a one-dimensional simple harmonic oscillator with state ket |q,t0=0> = exp(-ipq/hbar)|0>, parts (a) through (e) listed, with part (e) highlighted in yellow.


Homework Equations

The Attempt at a Solution


Handwritten derivation of a coherent state problem in quantum mechanics, with equations for dp/dt, dx/dt, x(t), <x(t)>, <p(t)> and expectation values, labelled parts (a) to (e).


These are what i solved except (e), I have no idea how to solve (e).
 
Given you have done parts a) to d), part e) shouldn't be any harder.

What's the definition of an eigenstate?