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 language | English |
|---|---|
| Pages (from-to) | 827-840 |
| Number of pages | 14 |
| Journal | Modern Physics Letters A |
| Volume | 19 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2004 Apr 10 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - A new symmetric expression of Weyl ordering
AU - Fujii, Kazuyuki
AU - Suzuki, Tatsuo
PY - 2004/4/10
Y1 - 2004/4/10
N2 - 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.
AB - 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.
KW - Difference operator
KW - Harmonic oscillator
KW - Quantization
KW - Stirling number
KW - Weyl ordering
UR - http://www.scopus.com/inward/record.url?scp=2142713819&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=2142713819&partnerID=8YFLogxK
U2 - 10.1142/S021773230401374X
DO - 10.1142/S021773230401374X
M3 - Article
VL - 19
SP - 827
EP - 840
JO - Modern Physics Letters A
JF - Modern Physics Letters A
SN - 0217-7323
IS - 11
ER -