Quantum oscillator

  • Thread starter nolanp2
  • Start date
  • #1
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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 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
 

Answers and Replies

  • #2
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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
 

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