|
| related topics |
| {group, space, representation} |
| {operator, operators, space} |
| {theory, mechanics, state} |
| {energy, gaussian, time} |
| {particle, mechanics, theory} |
| {classical, space, random} |
| {observables, space, algebra} |
| {vol, operators, histories} |
| {equation, function, exp} |
| {field, particle, equation} |
| {measurement, state, measurements} |
|
Theory of hybrid systems. I. The operator formulation of classical
mechanics and semiclassical limit
S. Prvanovic, Z. Maric
abstract: The algebra of polynomials in operators that represent generalized coordinate
and momentum and depend on the Planck constant is defined. The Planck constant
is treated as the parameter taking values between zero and some nonvanishing
$h_0$. For the second of these two extreme values, introduced operatorial
algebra becomes equivalent to the algebra of observables of quantum mechanical
system defined in the standard manner by operators in the Hilbert space. For
the vanishing Planck constant, the generalized algebra gives the operator
formulation of classical mechanics since it is equivalent to the algebra of
variables of classical mechanical system defined, as usually, by functions over
the phase space. In this way, the semiclassical limit of kinematical part of
quantum mechanics is established through the generalized operatorial framework.
- oai_identifier:
- oai:arXiv.org:quant-ph/0103044
- categories:
- quant-ph
- comments:
- 14 pages, LaTeX
- arxiv_id:
- quant-ph/0103044
- created:
- 2001-03-09
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