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New General Approach for Normally Ordering Coordinate-Momentum Operator Functions.
- Source :
-
International Journal of Theoretical Physics . Dec2016, Vol. 55 Issue 12, p5348-5355. 8p. - Publication Year :
- 2016
-
Abstract
- By virtue of integration technique within ordered product of operators and Dirac's representation theory we find a new general formula for normally ordering coordinate-momentum operator functions, that is $f(g\hat {{Q}}+h\hat {P})= :\exp [\textstyle {g^{2}+h^{2} \over 4}\textstyle {{\partial ^{2}} \over {\partial (g\hat {{Q}}+h\hat {P})^{2}}}]f(g\hat {{Q}}+h\hat {P})$ :, where $\hat {Q}$ and $\hat {P}$ are the coordinate operator and momentum operator respectively, the symbol :: denotes normal ordering. Using this formula we can derive a series of new relations about Hermite polynomial and Laguerre polynomial, as well as some new differential relations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00207748
- Volume :
- 55
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- International Journal of Theoretical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 119455633
- Full Text :
- https://doi.org/10.1007/s10773-016-3155-z