Non-commutative harmonic oscillators and the connection problem for the heun differential equation

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Abstract

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.

Original languageEnglish
Pages (from-to)133-139
Number of pages7
JournalLetters in Mathematical Physics
Volume70
Issue number2
DOIs
Publication statusPublished - Dec 1 2004
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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