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

Masato Wakayama

研究成果: Contribution to journalArticle査読

6 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)69-73
ページ数5
ジャーナルProceedings of the Japan Academy Series A: Mathematical Sciences
89
6
DOI
出版ステータス出版済み - 6 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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