Quantum systems with finite Hilbert space and Chebyshev polynomials

Quantum systems with finite Hilbert space and Chebyshev polynomials Finite quantum systems are considered and the Heisenberg–Weyl group of discrete displacements in the Z ( d )× Z ( d ) phase space is studied. Matrix elements of various operators are calculated and the result is given in terms of Chebyshev polynomials and their derivatives. The SL(2, Z ( d )) group of transformations in the phase space is studied. The general theory is applied in the context of spherical harmonics and provides a mathematical framework for the study of the angle–angular momentum quantum phase space. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

Quantum systems with finite Hilbert space and Chebyshev polynomials

Loading next page...
 
/lp/elsevier/quantum-systems-with-finite-hilbert-space-and-chebyshev-polynomials-BuHfStvzBs
Publisher
Elsevier
Copyright
Copyright © 2001 Elsevier Science B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/S0377-0427(00)00682-8
Publisher site
See Article on Publisher Site

Abstract

Finite quantum systems are considered and the Heisenberg–Weyl group of discrete displacements in the Z ( d )× Z ( d ) phase space is studied. Matrix elements of various operators are calculated and the result is given in terms of Chebyshev polynomials and their derivatives. The SL(2, Z ( d )) group of transformations in the phase space is studied. The general theory is applied in the context of spherical harmonics and provides a mathematical framework for the study of the angle–angular momentum quantum phase space.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 1, 2001

References

  • J. Phys. A
    Vourdas, A.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off