Electronic ISBN:  9780821877517 
Product Code:  CONM/160.E 
List Price:  $67.00 
MAA Member Price:  $60.30 
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Book DetailsContemporary MathematicsVolume: 160; 1994; 310 ppMSC: 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.
ReadershipPure mathematicians, applied mathematicians, and theoretical physicists.

Table of Contents

Articles

B. AbrahamShrauner 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 GonzálezLópez, Niky Kamran and Peter J. Olver  Quasiexact 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 timedependent 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  Manyelectron correlation problem and Lie algebras [ MR 1277384 ]

Mikhail A. Shifman  Quasiexactlysolvable spectral problems and conformal field theory [ MR 1277385 ]

Alexander Turbiner  Liealgebras and linear operators with invariant subspaces [ MR 1277386 ]


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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.
Pure mathematicians, applied mathematicians, and theoretical physicists.

Articles

B. AbrahamShrauner 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 GonzálezLópez, Niky Kamran and Peter J. Olver  Quasiexact 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 timedependent 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  Manyelectron correlation problem and Lie algebras [ MR 1277384 ]

Mikhail A. Shifman  Quasiexactlysolvable spectral problems and conformal field theory [ MR 1277385 ]

Alexander Turbiner  Liealgebras and linear operators with invariant subspaces [ MR 1277386 ]