A new symmetric expression of Weyl ordering

Kazuyuki Fujii, Tatsuo Suzuki

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

For the creation operator a† and the annihilation operator a of a harmonic oscillator, we consider Weyl ordering expression of (a†a) n and obtain a new symmetric expression of Weyl ordering w.r.t. a†a ≡ N and aa† = N + 1 where N is the number operator. Moreover, we interpret intertwining formulas of various orderings in view of the difference theory. Then we find that the noncommutative parameter corresponds to the increment of the difference operator w.r.t. variable N. Therefore, quantum (noncommutative) calculations of harmonic oscillators are done by classical (commutative) ones of the number operator by using the difference theory. As a by-product, nontrivial relations including the Stirling number of the first kind are also obtained.

Original languageEnglish
Pages (from-to)827-840
Number of pages14
JournalModern Physics Letters A
Volume19
Issue number11
DOIs
Publication statusPublished - 2004 Apr 10
Externally publishedYes

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harmonic oscillators

Keywords

  • Difference operator
  • Harmonic oscillator
  • Quantization
  • Stirling number
  • Weyl ordering

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Nuclear and High Energy Physics

Cite this

A new symmetric expression of Weyl ordering. / Fujii, Kazuyuki; Suzuki, Tatsuo.

In: Modern Physics Letters A, Vol. 19, No. 11, 10.04.2004, p. 827-840.

Research output: Contribution to journalArticle

Fujii, Kazuyuki ; Suzuki, Tatsuo. / A new symmetric expression of Weyl ordering. In: Modern Physics Letters A. 2004 ; Vol. 19, No. 11. pp. 827-840.
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