**Contemporary Mathematics**

Volume: 160;
1994;
310 pp;
Softcover

MSC: Primary 17; 81; 33;

**Print ISBN: 978-0-8218-5169-2
Product Code: CONM/160**

List Price: $72.00

AMS Member Price: $57.60

MAA Member Price: $64.80

**Electronic ISBN: 978-0-8218-7751-7
Product Code: CONM/160.E**

List Price: $67.00

AMS Member Price: $53.60

MAA Member Price: $60.30

# Lie Algebras, Cohomology, and New Applications to Quantum Mechanics

Share this page *Edited by *
*Niky Kamran; Peter J. Olver*

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

## Lie Algebras, Cohomology, and New Applications to Quantum Mechanics

- Contents v6 free
- Preface vii8 free
- Hidden symmetries of differential equations 110 free
- Algebraic methods in scattering 1524
- Exact solutions to operator differential equations 3140
- The algebra of tensor operators for the unitary groups 4756
- Lie groups and probability 5968
- Coherent tensor operators 7584
- Uq(sl(2)) and q-special functions 8594
- The group representation matrix in quantum mechanical scattering 101110
- Quasi-exact solvability 113122
- Quantization and deformation of Lie algebras 141150
- Algebraic theory 151160
- The time-dependent Schrödinger equation in multidimensional integrable evolution equations 173182
- Models of q-algebra representations: Matrix elements of Uq(su2) 191200
- Many-electron correlation problem and Lie algebras 209218
- Quasi-exactly-solvable spectral problems and conformal field theory 237246
- Lie-algebras and linear operators with invariant subspaces 263272