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The Invariant Eigen-Operator Method for Hamiltonians with Coordinates-Coordinates Coupling Terms

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Abstract

In this paper, we apply the method of “invariant eigen-operator” to study the Hamiltonian of harmonic oscillator with couplings and derive their invariant eigen-operator. We first discuss decoupling of coupled harmonic oscillators with the two different quality and frequencies. And then, we propose an operator Hamiltonian to describe the linear lattice chain with Born–von Karman boundary condition. The vibrating spectrum is thus obtained. The results show that, for the system of coupled harmonic oscillators by coordinate coupling or momentum coupling, the invariant eigen operator \(\hat{Q}\) of system always has the form of \(\hat{Q}=\sum_{j}g_{j}\hat{x}_{j}\) or \(\hat{Q}=\sum_{j}\lambda_{j}\hat{p}_{j}\) .

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Authors and Affiliations

  1. Education College, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China

    Yong-mei Liu

  2. College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang, Jiangxi, 33002, China

    Ying-hua Ji

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  1. Yong-mei Liu
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  2. Ying-hua Ji
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Correspondence to Ying-hua Ji.

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Liu, Ym., Ji, Yh. The Invariant Eigen-Operator Method for Hamiltonians with Coordinates-Coordinates Coupling Terms. Int J Theor Phys 48, 1500–1507 (2009). https://doi.org/10.1007/s10773-008-9922-8

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  • DOI: https://doi.org/10.1007/s10773-008-9922-8

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