Coupled harmonic oscillator systems: Improved algebraic decoupling approach

We present a novel explicit decoupling procedure that leads to exact solutions of the Schrodinger equation for N harmonic oscillators in the presence of general bilinear perturbing potentials. This generalizes previous work, which was restricted to orthogonal transformations with conditions imposed on the perturbing terms. It is shown that the formalism is sufficiently general to embrace both stationary-state and resonance-state problems and, in particular, we include exact model calculations of a free electron interacting with a lattice and a discussion of an application to an ideal ion trap.