CONTINUOUS-REPRESENTATION THEORY. III. ON FUNCTIONAL QUANTIZATION OF CLASSICAL SYSTEMS
>The form of Schroedinger's equation in a continuous representution is indicated for general systems and analyzed in detail for elementary Bose and Fermi systems, for which illustrative solutions are given. For any system a natural continuous representation exists in which state vectors are expressed as continuous, bounded functions of the corresponding classical variables. The natural continuous representation is generated by a suitable set S of unit vectors labeled by classical variables for which, for the system in question, the qaantum action functional restricted to the domain S is equivalent to the classical action. When a classical action is viewed in this manner it contains considerable information about the quantum system. Augmenting the classical action with some physical significance of its variables it is proved that the classical theory virtually determines the quantum theory for the Bose system, while it uniqUely determines the quantum theory for the Fermi system. (auth)
- Research Organization:
- Bell Telephone Labs., Murray Hill. N.J.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-18-010999
- OSTI ID:
- 4077669
- Journal Information:
- J. Math, Phys.(N.Y.), Vol. Vol: 5; Other Information: Orig. Receipt Date: 31-DEC-64
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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