Non-commutative Harmonic Oscillators and the Connection Problem for the Heun Differential Equation
- Hiroyuki Ochiai
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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.
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- Non-commutative Harmonic Oscillators and the Connection Problem for the Heun Differential Equation
Letters in Mathematical Physics
Volume 70, Issue 2 , pp 133-139
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- Kluwer Academic Publishers
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- Heun’s equation
- algebraic solution
- accessory parameter
- apparent singularity
- Hiroyuki Ochiai (1)
- Author Affiliations
- 1. Department of Mathematics, Nagoya University, Chikusa, Nagoya, 464-8602, Japan