Solving Quantum Oscillator w/ Coherent State [alpha(0)>

[nolanp2]

Homework Statement

given a harmonic oscillator initially in a coherent state [alpha(0)>, alpha = pe^(iv) find the state of the system at time t.

Homework Equations

H = hw/2pi(N+1/2) for harmonic oscillator
given answer: state at time t = e^(-iwt/2)[alpha(t)>

The Attempt at a Solution

i've used the schro eqn to find the state but my answer is only dependant on [alpha(0)> rather than [alpha(t)> i figure i must be setting up the equation wrong but i can't figure out where. I'm not looking for a full solution, just want to know how exactly the coherent state [alpha> will vary in time here. any hints would be appreciated

 

[Marco_84]

i think you have to use just the time evolution operator which is just:

U(t)=exp(iHt)
and it satisfy UU*=U*U=1 since H is hermitian...
this.
U(t)|q>=U(t)exp(iqp)U*(t)|0>...
and go on.
Note that this kind of potential it is really peculiar since it gives you coherent states.

bye
marco