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Journal of Physics A Mathematical and General

Exact Schrödinger wavefunctions ofN-coupled time-dependent harmonic oscillators

Min-Ho Lee

Published Oct 31, 2001• 4 citations
Publisher

Abstract

For N -coupled time-dependent harmonic oscillators with any couplings coordinates and momentum, we have derived the primary invariant and the generalized (Lewis and Riesenfeld) invariant represented in terms of the classical solution matrix of Hamilton's oscillator equation. Using the Lewis and Riesenfeld invariant method and exploiting the properties of the symplectic matrix we have obtained the exact Schrödinger wavefunctions for the oscillators.

DOI
10.1088/0305-4470/34/44/309

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For N -coupled time-dependent harmonic oscillators with any couplings coordinates and momentum, we have derived the primary invariant and the generalized (Lewis and Riesenfeld) invariant represented in terms of the classical solution matrix of Hamilton's oscillator equation. Using the Lewis and Riesenfeld invariant method and exploiting the properties of the symplectic matrix we have obtained the exact Schrödinger wavefunctions for the oscillators.
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By making use of linear and quadratic invariants and the invariant operator formulation of Lewis and Riesenfeld, the complete exact solutions of the Schrödinger equation for the generalized time-dependent harmonic oscillator are obtained. It is shown that the general solution of the system under consideration contains both the discrete and continuous spectrum. The connection between linear and quadratic invariants and their corresponding eigenstates via time-dependent auxiliary equations is also established.