Open AccessOperator-ordering identities for mutual transformation of power of coordinate-momentum operators obtained by a new concise method
Author(s) -
Hong-Yi Fan,
Lou Sen-Yue,
Peng-Fei Zhang
Publication year - 2015
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.64.160302
Subject(s) - operator (biology) , hermite polynomials , displacement operator , operator theory , mathematics , power series , quantization (signal processing) , transformation (genetics) , pure mathematics , algebra over a field , computer science , mathematical analysis , quasinormal operator , algorithm , finite rank operator , banach space , biochemistry , chemistry , repressor , transcription factor , gene
Since the foundation of quantum mechanics, operator-ordering identities for mutual transformation of power of coordinate-momentum operators have been a fundamental and tough topic. To the best of our knowledge, this topic has not been tackled smoothly because there is no elegant and direct way to investigate it. In this paper we report a very concise and novel method to handle this topic, i.e., we employ the generating function of two-variable Hermite polynomial and the characteristics of ordered operators to derive a series of operator-ordering identities for mutual transformation of power of coordinate-momentum operators: they surly possess potential applications. The essence of our method lies in the fact that coordinate-momentum operators can be permutable within ordered product of operators, just as the scenarios in P-Q ordering, Q-P ordering and Weyl ordering. We also derive the integration transformation formula about two-variable Hermite polynomial in phase space. The correspondence relation between operator ordering and quantization recipe is established. The beauty of theoretical physics is embodied extensively in the paper.