"Consider the quantum mechanical harmonic oscillator. Let the energy eigenstates and eigenvalues of this system be given by |ψ_n> and E_n = (n + 1/2)ħω, respectively.
At t=0, the state of a particle in this potential is given by: |ψ_a> = 1/√2 (|ψ_0> + |ψ_1>)
Determine ω_p (angular frequency for the probability density of a superposition of two energy eigenstates) for |ψ_a>. How is it related to ω, the frequency of the harmonic oscillator potential?"
Only one I can think of is that |ψ_n> ≈ sin(nπx/a), but that's for an infinite square well I think. Other than that I have no idea.
The Attempt at a Solution
I really am not sure even where to start with this. I'm guessing that if we were to find the probability density of |ψ_a> we could then somehow get the angular frequency ω_p? I think a big problem is that I'm not sure how we would connect an energy eigenvalue and eigenstate. Also I'm not really sure how the frequency of the harmonic oscillator potential comes into play...