Article,
Time-dependent coupled harmonic oscillators: Classical and quantum solutions
INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS, (2014)
DOI: 10.1142/S0218301314500487
Abstract
In this work we present the classical and quantum solutions for an
arbitrary system of time-dependent coupled harmonic oscillators, where
the masses (m), frequencies (omega) and coupling parameter (k) are
functions of time. To obtain the classical solutions, we use a
coordinate and momentum transformations along with a canonical
transformation to write the original Hamiltonian as the sum of two
Hamiltonians of uncoupled harmonic oscillators with modified
time-dependent frequencies and unitary masses. To obtain the exact
quantum solutions we use a unitary transformation and the Lewis and
Riesenfeld (LR) invariant method. The exact wave functions are obtained
by solving the respective Milne-Pinney (MP) equation for each system. We obtain the solutions for the system with m(1) = m(2) = m(0)e(gamma t), omega(1) = omega(0)1e(-gamma t/2), omega(2) = omega(0)2e(-gamma t/2) and k = k(0).
