Coupled quantum harmonic oscillators

[dflake]

Hi folks,
I have to solve an exercise about two oscillators whose Hamiltonian is
H = 1/2 (m w^2 q1^2 + m mu^2 w^2 q2^2 + m lambda^2 w^2 q1 q2)
I successfully found the unitary transformation that decouples the problem, but I am also asked to use the Adiabatic Method to find approximate solutions of the eigenfunctions and eigenvalues of H, and find the values of lambda and mu that allow one to use such a method.
As the Hamiltonian is time independent, I don't understand how should I apply the adiabatic scheme here.
Does anyone have hints? Is this problem treated in any book you know?
Thanks a lot,
D

 

[azntoon]

avide. §§ COMUpdateWell, I found the answer to my own question. Adiabatic Theorem can be applied here as one of the eigenvalues of the Hamiltonian is time-dependent (the frequency of the oscillator which depends on lambda and mu).Hope this helps someone else. Davide.