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

Find the energy levels and the wave functions of two harmonic oscillators of mass [tex]m_1[/tex]and [tex]m_2[/tex],

having identical frequencies [tex]\omega[/tex], and coupled by the interaction [tex]\frac{1}{2}k(x_{1}^{2}-x_{2}^{2})^2[/tex]

2. Relevant equations

Schrodinger equation.

3. The attempt at a solution

My first question is, if the interaction term as it is given makes sense, as it is not of the characteristic of energy/ potential (unit is different!). Therefore i cannot see how to put it into the hamiltonian.

If i just take the interaction terms as it is and add it to the sum of two harmonic oscillators, the term gets long and i can not decouple this hamiltonian

Please give me any hint on this problems. Thank you very much in advance!

**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: Coupled Harmonic Oscillator

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