A new symmetric expression of Weyl ordering

Kazuyuki Fujii, Tatsuo Suzuki

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Issue number11
Publication statusPublished - 2004 Apr 10
Externally publishedYes


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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics
  • Physics and Astronomy(all)


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