# General Harmonic Oscillator

1. Apr 3, 2014

### helpppmeee

Edit: Problem solved please disregard this post

1. The problem statement, all variables and given/known data
A particle in the harmonic oscillator potential has the initial wave function $\Psi$(x, 0) = ∑(from n = 0 to infinity) Cnψn(x) where the ψ(x) are the (normalized) harmonic oscillator eigenfunctions and the coefficients are given by the expression Cn = 1/(√(2^(n=1))). What is the probability that a measurement of the oscillator's energy at an arbitrary time t>0 will yield a result greater than 2(hbar)ω.

2. Relevant equations
En = (n + 1/2)(hbar)ω

3. The attempt at a solution
I believe I can attempt the answer. The P(E>2(hbar)ω) is when En = 2(hbar)ω so ∴, n > 2 is when En = 2(hbar)ω. So, from 2 to infinite integers, we have the potential energies according to the equation $\Psi$(x, 0) = ∑(from n = 0 to infinity) Cnψn(x). So therefore, I believe that the integral of ($\Psi$(x, 0))^2 will give me my probability of finding the energy. So therefore, P(E>2(hbar)ω) = 1 - P(E≤2(hbar)ω) where P(E≤2(hbar)ω) = C1ψ1 + C0ψ0. I just can't seem to figure out what ψ is.

Last edited: Apr 3, 2014
2. Apr 3, 2014

### helpppmeee

Really? nobody can help?