(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a particle is confined in a one dimensional harmonic oscillator potential, find the matrix representation of the momentum operator in the basis of the eigenvectors of the Hamiltonian.

2. Relevant equations

Potential: V(x) = 0.5 m w^2 x^2 where m is the mass of the particle and w is the angular frequency

Schrodinger equation: H |psi> = E |psi> where H is the Hamiltonian operator, E are its eigenvalues (or the energies of the system), and |psi> are its eigenvectors (or the stationary states of the system).

E = h w (n + 0.5) where h is the reduced Planck constant, w is the same as in V(x), and n = 1, 2, 3, 4, ...

|psi> = http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator#Hamiltonian_and_energy_eigenstates (look under topic 1.1: Hamiltonian and energy eigenstates)

3. The attempt at a solution

This was a question on my midterm exam, and I had absolutely no clue how to tackle it. I still don't. It won't be necessary to do the algebra, but can someone just sketch out the method of obtaining the solution for me?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the momentum operator matrix of the harmonic oscillator

**Physics Forums | Science Articles, Homework Help, Discussion**