Representation of a One-Dimensional Motion in a Morse Potential by a Quadratic Hamiltonian

摘要

There is considerable current interest in the dynamics of anharmonic oscillators. The algebraic hamiltonian for the Morse oscillator which is discussed here is useful not only for such studies but also for elucidating the behavior of systems of coupled anharmonic oscillators. Furthermore, the mathematical simplicity of handling a quadratic hamiltonian has made the harmonic oscillator the favorite model for a variety of applications. Much of this simplicity is retained by the present hamiltonian which should therefore lend itself to similar purposes. An extensive discussion of the algebraic description of three-dimensional oscillator. A representation of the algebraic hamiltonian for the anharmonic Morse oscillator as a quadratic form, H=homega(1/2 p squared +1/2 Q2), where P and Q are operators is derived. The commutator of P and Q is an operator that tends to i (times the identity operator) in the harmonic limit. Coherent states and anharmonic normal modes for a linear triatomic molecule are discussed as potential applications.