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Jilin Normal University Journal

Deriving the Energy-level Gap of Three-dimensional Coordinate-momentum Coupled Quantum Harmonic Oscillators by Invariant Eigen-operator Method

Hongyan Liu

Published Jan 1, 2009• 0 citations
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Abstract

The energy levels for three-dimensional coordinate-momentum coupled quantum harmonic oscillators are presented by using invariant eigen-operator method.The results show that the energy-level gaps are same for different coordinate-momentum coupled form of three-dimensional quantum harmonic oscillators.

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The normal frequencies and its corresponding normal coordinates and conjugate momentums of the n-module coupled harmonic oscillators quantum system are derived by using the invariant eigen-operator method.The Hamiltonian of the system is decoupled and then the visible analytic solution of normal frequencies in the system is obtained.The analytic solution of wave function of the system in the coordinate representation is deduced.Through the discussion of the coupling coefficients of different situations,we have concluded that the coupled harmonic oscillator systems with the n-module momentum or coordinates are just special cases of the system under study.