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<p>We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the <i>SU</i>(1,1) and <i>SU</i>(2) groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its Hamiltonian in terms of the boson generators of the <i>SU</i>(1,1) and <i>SU</i>(2) groups. We use the one boson and two boson realizations of the <i>su</i>(1,1) Lie algebra, and the one boson realization of the <i>su</i>(2) Lie algebra to apply three tilting transformations to diagonalize the original Hamiltonian. These transformations allow us to obtain the energy spectrum and eigenfunctions of the isotropic and the anisotropic cases, from which the particular expected results are obtained for the cases where the coupling is neglected.</p>

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Exact solution of the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators

  • 期刊论文

  • 发表日期：

    2025年7月20日

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  • J. C. Vega,
  • D. Ojeda-Guillén,
  • R. D. Mota

摘要

We study the isotropic and anisotropic Hamiltonian of two coupled harmonic oscillators from an algebraic approach of the SU(1,1) and SU(2) groups. In order to obtain the energy spectrum and eigenfunctions of this problem, we write its Hamiltonian in terms of the boson generators of the SU(1,1) and SU(2) groups. We use the one boson and two boson realizations of the su(1,1) Lie algebra, and the one boson realization of the su(2) Lie algebra to apply three tilting transformations to diagonalize the original Hamiltonian. These transformations allow us to obtain the energy spectrum and eigenfunctions of the isotropic and the anisotropic cases, from which the particular expected results are obtained for the cases where the coupling is neglected.