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Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
 
Front Cover for Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
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Softcover ISBN: 978-0-8218-5169-2
Product Code: CONM/160
310 pp 
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $57.60
Electronic ISBN: 978-0-8218-7751-7
Product Code: CONM/160.E
310 pp 
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $53.60
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Front Cover for Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
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  • Front Cover for Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
  • Back Cover for Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
Lie Algebras, Cohomology, and New Applications to Quantum Mechanics
Available Formats:
Softcover ISBN:  978-0-8218-5169-2
Product Code:  CONM/160
310 pp 
List Price: $72.00
MAA Member Price: $64.80
AMS Member Price: $57.60
Electronic ISBN:  978-0-8218-7751-7
Product Code:  CONM/160.E
310 pp 
List Price: $67.00
MAA Member Price: $60.30
AMS Member Price: $53.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $108.00
MAA Member Price: $97.20
AMS Member Price: $86.40
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1601994
    MSC: Primary 17; 81; 33;

    This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a “hidden” symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, \(q\)-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents a look at some of the current developments in this extraordinarily rich and vibrant area.

    Readership

    Pure mathematicians, applied mathematicians, and theoretical physicists.

  • Table of Contents
     
     
    • Articles
    • B. Abraham-Shrauner and A. Guo - Hidden symmetries of differential equations [ MR 1277371 ]
    • Y. Alhassid - Algebraic methods in scattering [ MR 1277372 ]
    • Carl M. Bender - Exact solutions to operator differential equations [ MR 1277373 ]
    • L. C. Biedenharn - The algebra of tensor operators for the unitary groups [ MR 1277374 ]
    • Philip Feinsilver - Lie groups and probability [ MR 1277375 ]
    • Dan Flath - Coherent tensor operators [ MR 1277376 ]
    • Roberto Floreanini and Luc Vinet - ${\scr U}_q({\rm sl}(2))$ and $q$-special functions [ MR 1277377 ]
    • Joseph N. Ginocchio - The group representation matrix in quantum mechanical scattering [ MR 1277378 ]
    • Artemio González-López, Niky Kamran and Peter J. Olver - Quasi-exact solvability [ MR 1277379 ]
    • Palle E. T. Jorgensen - Quantization and deformation of Lie algebras [ MR 1277380 ]
    • Francesco Iachello - Algebraic theory [ MR 1277381 ]
    • D. J. Kaup - The time-dependent Schrödinger equation in multidimensional integrable evolution equations [ MR 1277382 ]
    • E. G. Kalnins, Willard Miller, Jr. and Sanchita Mukherjee - Models of $q$-algebra representations: matrix elements of $U_q({\rm su}_2)$ [ MR 1277383 ]
    • Josef Paldus - Many-electron correlation problem and Lie algebras [ MR 1277384 ]
    • Mikhail A. Shifman - Quasi-exactly-solvable spectral problems and conformal field theory [ MR 1277385 ]
    • Alexander Turbiner - Lie-algebras and linear operators with invariant subspaces [ MR 1277386 ]
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Volume: 1601994
MSC: Primary 17; 81; 33;

This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a “hidden” symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, \(q\)-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents a look at some of the current developments in this extraordinarily rich and vibrant area.

Readership

Pure mathematicians, applied mathematicians, and theoretical physicists.

  • Articles
  • B. Abraham-Shrauner and A. Guo - Hidden symmetries of differential equations [ MR 1277371 ]
  • Y. Alhassid - Algebraic methods in scattering [ MR 1277372 ]
  • Carl M. Bender - Exact solutions to operator differential equations [ MR 1277373 ]
  • L. C. Biedenharn - The algebra of tensor operators for the unitary groups [ MR 1277374 ]
  • Philip Feinsilver - Lie groups and probability [ MR 1277375 ]
  • Dan Flath - Coherent tensor operators [ MR 1277376 ]
  • Roberto Floreanini and Luc Vinet - ${\scr U}_q({\rm sl}(2))$ and $q$-special functions [ MR 1277377 ]
  • Joseph N. Ginocchio - The group representation matrix in quantum mechanical scattering [ MR 1277378 ]
  • Artemio González-López, Niky Kamran and Peter J. Olver - Quasi-exact solvability [ MR 1277379 ]
  • Palle E. T. Jorgensen - Quantization and deformation of Lie algebras [ MR 1277380 ]
  • Francesco Iachello - Algebraic theory [ MR 1277381 ]
  • D. J. Kaup - The time-dependent Schrödinger equation in multidimensional integrable evolution equations [ MR 1277382 ]
  • E. G. Kalnins, Willard Miller, Jr. and Sanchita Mukherjee - Models of $q$-algebra representations: matrix elements of $U_q({\rm su}_2)$ [ MR 1277383 ]
  • Josef Paldus - Many-electron correlation problem and Lie algebras [ MR 1277384 ]
  • Mikhail A. Shifman - Quasi-exactly-solvable spectral problems and conformal field theory [ MR 1277385 ]
  • Alexander Turbiner - Lie-algebras and linear operators with invariant subspaces [ MR 1277386 ]
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