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

Research output: Contribution to journalArticle

11 Citations (Scopus)


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
Issue number2
Publication statusPublished - Dec 1 2004
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this