# Quantum oscillator

1. Jan 16, 2008

### nolanp2

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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 cant 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

2. Jan 16, 2008

### Marco_84

i think you have to use just the time evolution operator wich 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