# Sudden perturbation approximation for oscillator

1. May 14, 2008

### jsc314159

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

An oscillator is in the ground state of $$H = H^0 + H^1$$, where the time-independent perturbation $$H^1$$ is the linear potential (-fx). It at t = 0, $$H^1$$ is abruptly turned off, determine the probability that the system is in the nth state of $$H^0$$ .

2. Relevant equations

First, since the perturbation is turned off abruptly, the sudden perturbation approximation may be used.

$$P(n) = |<n|n^0>|^2$$.

3. The attempt at a solution

I am not sure where to start. Is this best done in the coordinate basis or the energy basis?

In either basis, I need some type of representation of |n> but I am not sure where to start with that.

$$n^0$$ can be represented as |0> in the energy basis or $$\psi(t) = A_0 * e^{y{2}}$$ in the coordinate basis.

jsc

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