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Coupled Harmonic Oscillator

  1. May 3, 2007 #1
    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!
    Last edited: May 3, 2007
  2. jcsd
  3. May 15, 2007 #2
    No one can help ? :)

    Now I got that from Prof. that it was given wrong, it must bu (x1-x2)^2 in the interaction term, but if it is like above given interaction term, is it right? I mean is such an interaction term possible?
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