(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

relative coordinate :: x=x1-x2

CM position :: X

3. 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

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# Homework Help: Coupled harmonic oscillators QM

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