|
| related topics |
| {state, states, coherent} |
| {cos, sin, state} |
| {equation, function, exp} |
| {operator, operators, space} |
| {states, state, optimal} |
| {vol, operators, histories} |
| {group, space, representation} |
| {algorithm, log, probability} |
| {classical, space, random} |
| {let, theorem, proof} |
|
Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the
Intervall [-1,1]
Thomas Appl, Diethard H. Schiller
abstract: The quantization of phase is still an open problem. In the approach of
Susskind and Glogower so called cosine and sine operators play a fundamental
role. Their eigenstates in the Fock representation are related with the
Chebyshev polynomials of the second kind. Here we introduce more general cosine
and sine operators whose eigenfunctions in the Fock basis are related in a
similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1].
To each polynomial set defined in terms of a weight function there corresponds
a pair of cosine and sine operators. Depending on the symmetry of the weight
function we distinguish generalized or extended operators. Their eigenstates
are used to define cosine and sine representations and probability
distributions. We consider also the inverse arccosine and arcsine operators and
use their eigenstates to define cosine-phase and sine-phase distributions,
respectively. Specific, numerical and graphical results are given for the
classical orthogonal polynomials and for particular Fock and coherent states.
- oai_identifier:
- oai:arXiv.org:quant-ph/0503147
- categories:
- quant-ph
- comments:
- 1 tex-file (24 pages), 11 figures
- doi:
- 10.1088/0305-4470/38/29/005
- arxiv_id:
- quant-ph/0503147
- created:
- 2005-03-16
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