New approach for normally ordering coordinate-operator functions
| Autor: | Hong-Yi Fan, Hong-qi Li, Xing-lei Xu, Shi-Min Xu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Operator (computer programming) Hermite polynomials Series (mathematics) Dirac (video compression format) Product (mathematics) Laguerre polynomials Electrical and Electronic Engineering Representation theory Atomic and Molecular Physics and Optics Differential (mathematics) Electronic Optical and Magnetic Materials Mathematics |
| Zdroj: | Optik. 127:9961-9965 |
| ISSN: | 0030-4026 |
| DOI: | 10.1016/j.ijleo.2016.07.064 |
| Popis: | By virtue of the integration technique within ordered product of operators and Dirac’s representation theory we find a new formula for normally ordering coordinate-operator functions, that is f ( Q ˆ ) = : exp ( 1 4 ∂ 2 ∂ Q ˆ 2 ) f ( Q ˆ ) : , where Q ˆ is the coordinate operator, the symbol : : denotes normal ordering. Using this formula we can arrange a given quantum operator function f ( Q ˆ ) in its normal ordering conveniently and fast. Furthermore, we can derive a series of new relations about Hermite polynomial and Laguerre polynomial, as well as some new differential relations. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect