Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra**The project supported by the Key Track Follow-Up Service Foundation of the State Education Commission of China and Science Foundation of the Liaoning Education Commission of China

Abstract

Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) ⊃ U(2).