Newton-Leibniz integration for ket-bra operators in quantum mechanics (IV)-Integrations within Weyl ordered product of operators and their applications
- Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China)
We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] applied to tackling Newton-Leibniz integration over ket-bra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol is introduced to find the Wigner operator's Weyl ordering form {delta}(p,q) = {delta}(p - P){delta}(q - Q) , and to find operators' Weyl ordered expansion formula. A remarkable property is that Weyl ordering of operators is covariant under similarity transformation, so it has many applications in quantum statistics and signal analysis. Thus the invention of the IWWOP technique promotes the progress of Dirac's symbolic method.
- OSTI ID:
- 21077690
- Journal Information:
- Annals of Physics (New York), Vol. 323, Issue 2; Other Information: DOI: 10.1016/j.aop.2007.06.003; PII: S0003-4916(07)00088-7; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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