Coupled Q. Harmonic Oscillators

  1. My quantum mechanics teacher give me the following problem:

    "Find eigenvalues of the following system: two different particles of mass m in a harmonic oscillator coupled by attractive potential V(x1,x2)=beta*abs(x1-x2)."

    Now, I know that standard solving method for this kind of problem is to substitue x1 and x2 with appropriate expressions.

    Using reduced mass, i can transform V(x1,x2)=beta*abs(x1-x2) in V(y)=something*abs(y).

    This problem, a part the "abs", is similar to a harmonic oscillator in a electric field...but is only similar...i don't know how to manage the "abs". I have thought that the only method for removing abs is to replace y with something always positive (or negative) but my little brain can't find the solution!

    Can anyone help me??

    Thank you in advance
  2. jcsd
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