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## Homework Statement

I have the first three states of the harmonic oscillator, and I need to know the amplitudes for the states after the potential is dropped.

## Homework Equations

[itex]u_{0}=(\frac{1}{\pi a^{2}})^{\frac{1}{4}} e^{{\frac{-x^2}{2a^2}}}[/itex]

[itex]u_{1}=(\frac{4}{\pi})^{\frac{1}{4}} (\frac{1}{a^2})^\frac{3}{4} x e^{({\frac{-x^2}{2a^2}})}[/itex]

[itex]u_{2}=(\frac{1}{4\pi a^2})^{\frac{1}{4}} (\frac{2x^2}{a^2}-1) e^{{\frac{-x^2}{2a^2}}}[/itex]

Then, the potential is lowered suddenly, by setting [itex]\omega ' = \frac{\omega}{2}[/itex].

The system is then modelled with the expansion postulate, as a superposition of these three new states, with [itex]\omega'[/itex] in them.

The particle was originally in the ground state before the potential was lowered, so I have that:

[itex]C_{i}=\int u_{i}^* \psi dx[/itex]

Where [itex]\psi[/itex] represents the ground state function, as stated above, with [itex]\omega[/itex]. The states are real though, so the complex conjugate is unchanged from the normal state.

## The Attempt at a Solution

When I try to evaluate these integrals, I find that I can't actually do it. The problem is that the different symbols keep tripping me up... The ω and ω' values don't seem to gel.

Am I doing the physics wrong, or am I simple falling short on the maths?

Thanks, all.