Coupled Q. Harmonic Oscillators

filo85x

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