A New Symmetric Expression of Weyl Ordering

Details A New Symmetric Expression of Weyl Ordering A New Symmetric Expression of Weyl Ordering

2003-04-13

arxiv.org/abs/quant-ph/0304094v2

Mod.Phys.Lett. A19 (2004) 827-840

Physics

Quantum Physics

15 pages, Latex2e, the title before replacement is "Orderings of Operators in Quantum Physics", new proofs by using a differen

Scientific paper

10.1142/S021773230401374X

For the creation operator $\adag $ and the annihilation operator $a$ of a harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$ and $a\adag =N+1$ 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.

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