Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun's differential equation

Masato Wakayama

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The non-commutative harmonic oscillator (NcHO) is a special type of selfadjoint ordinary differential operator with non-commutative coefficients. In the present note, we aim to provide a reasonable criterion that derives the simplicity of the lowest eigenvalue of NcHO. It actually proves the simplicity of the lowest eigenvalue for a large class of structure parameters. Moreover, this note describes a certain equivalence between the spectral problem of the NcHO (for the even parity) and existence of holomorphic solutions of Heun's ordinary differential equations in a complex domain. The corresponding Riemann scheme allows us to give another proof to the criterion.

Original languageEnglish
Pages (from-to)69-73
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume89
Issue number6
DOIs
Publication statusPublished - Jun 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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