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Homework Statement
Consider two coupled oscillators. The Hamiltonian is given as
H=p1^2/2m + p2^2/2m +1/2m*omega^2*[x1^2+x2^2+2*lambda*(x1-x2)^2]
Separate the center of mass and relative motion and find the eigenfunctions and eigenvalues.
Homework Equations
relative coordinate :: x=x1-x2
CM position :: X
The Attempt at a Solution
i assume that i have to reduce the 2 body to equivalent one body, using the fact that the potential only depends of the separation of the 2 particles x1-x2, that is, if V(x1,x2)=V(x1-x2)
now introduce 2 new variables,
x=x1-x2,
X=m1x1+m2x2/(m1+m2)
now introduce REDUCED MASS 1/mu:=1/m1+1/m2
not sure how to proceed