Non-commutative harmonic oscillators-II

Alberto Parmeggiani, Masato Wakayama

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We refine our study of the spectrum of non-commutative harmonic oscillators Q(x, Dx) = 1/2A(-∂x 2 + x2) + B(x∂x + 1/2), x ∈ ℝ, where A, B ∈ Mat2(ℝ) are constant 2 × 2 matrices such that A = tA > 0 (or <0) and B = -tB ≠ 0, and the Hermitian matrix A + iB > 0 (or <0). We introduce a new family of L2-bases and study the relation between the coefficients of the eigenfunction obtained by means of these bases, and the ones obtained by means of the bases introduced in [4]. We hence completely determine the spectrum and its multiplicity.

Original languageEnglish
Pages (from-to)669-690
Number of pages22
JournalForum Mathematicum
Volume14
Issue number5
DOIs
Publication statusPublished - Jan 1 2002

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Harmonic Oscillator
Eigenvalues and eigenfunctions
Eigenfunctions
Multiplicity
Coefficient
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Non-commutative harmonic oscillators-II. / Parmeggiani, Alberto; Wakayama, Masato.

In: Forum Mathematicum, Vol. 14, No. 5, 01.01.2002, p. 669-690.

Research output: Contribution to journalArticle

Parmeggiani, Alberto ; Wakayama, Masato. / Non-commutative harmonic oscillators-II. In: Forum Mathematicum. 2002 ; Vol. 14, No. 5. pp. 669-690.
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