Solving Psi(x,t) for a Harmonic Oscillator

[Talib]

Hello,

A harmonic oscillator is in the initial state:
Psi(x, 0) = Phi_n (x)
where Phi_n(x) is the nth solution of the time-independent Schr¨odinger equation.
What is Psi(x, t)?

Any clue?

Thanks

 

[quasar987]

Psi(x, t) is the solution of the time dependent Schrödinger equation (TDSE). The TDSE is a separable partial differential equation. More precisely, the solution to the TDSE is the product of the TISE and of [itex]\exp(iEt/\hbar)[/tex]:<br /> <br /> $$\Psi(x,t)=\psi(x)e^{iEt/\hbar}$$[/itex]

 

[Talib]

Thanks a lot :):)