Contemporary Mathematics 1994; 310 pp; softcover Volume: 160 ISBN10: 0821851691 ISBN13: 9780821851692 List Price: US$67 Member Price: US$53.60 Order Code: CONM/160
 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  B. AbrahamShrauner and A. Guo  Hidden symmetries of differential equations
 Y. Alhassid  Algebraic methods in scattering
 C. M. Bender  Exact solutions to operator differential equations
 L. C. Biedenharn  The algebra of tensor operators for the unitary groups
 P. Feinsilver  Lie groups and probability
 D. Flath  Coherent tensor operators
 R. Floreanini and L. Vinet  \({\scr U}_q(sl(2))\) and q special functions
 J. N. Ginocchio  The group representation matrix in quantum mechanical scattering
 A. GonzálezLópez, N. Kamran, and P. J. Olver  Quasiexact solvability
 P. E. Jorgensen  Quantization and deformation of Lie algebras
 F. Iachello  Algebraic theory
 D. J. Kaup  The timedependent Schrödinger equation in multidimensional integrable evolution equations
 E. G. Kalnins, W. Miller, Jr., and S. Mukherjee  Models of \(q\)algebra representations: Matrix elements of \(U_q(su_2)\)
 J. Paldus  Manyelectron correlation problem and Lie algebras
 M. A. Shifman  Quasiexactlysolvable spectral problems and conformal field theory
 A. Turbiner  Liealgebras and linear operators with invariant subspaces
