Quantum harmonic oscillator in electric field

[mbijei]

Homework Statement

There is a harmonic oscillator with charge q and sudenly we turn on external electric field E, which direction is the same as oscillator's. We need to find probability, that particles energy calculated in electric field will be in m state.
n=1, m=2

2. Homework Equations

The Attempt at a Solution

So I've solved Schrödinger's equation for harmonic oscillator in electric field and found needed energy eigenvalue, but I don't know how to find probability.

 

[vela]

How do you usually calculate probabilities in quantum mechanics? In other words, if the particle is in state $\lvert \psi \rangle$ and you want to know the probability you'll find it in state $\lvert \phi \rangle$, what do you do?

 

[mbijei]

That's the point, I don't have state vectors ∣ψ⟩ and ∣ϕ⟩. I only have Hamiltonian and energy eigenvalue.

 

[vela]

You said you solved the Schrödinger equation. How can you not have the state vectors?

 

[laimonel]

Could someone PLEASE explain this solution step by step? I have this very same problem (except both n and m are equal to 1) and i can't find any examples how to solve this kind of problems anywhere..

 

[vela]

No, that's not how it works here. We don't provide solutions. You need to try figure it out. That's how you learn.

 

[laimonel]

Well I've been trying since yesterday and I'm pretty frustrated by now. I've searched everywhere for at least one example on how to solve this kind of problem and found nothing. I'm probably not the brightest kid and i seem to be unable to figure it all out just by myself..