|Sep16-11, 07:33 AM||#1|
Coupled Q. Harmonic Oscillators
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
|coupled, harmonic, oscillator|
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