Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations
- CCAST (World Laboratory), P.O. Box 8730, Beijing 100080 (China)
- Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China)
- Intel Corporation 2200 Mission College Blvd., Santa Clara, CA 95052-8119 (United States)
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., |q><q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |><| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.
- OSTI ID:
- 20766990
- Journal Information:
- Annals of Physics (New York), Vol. 321, Issue 2; Other Information: DOI: 10.1016/j.aop.2005.09.011; PII: S0003-4916(05)00189-2; Copyright (c) 2005 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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