Algebraic approach to simple quantum systems

by Barry G. Adams

This monograph is primarily aimed at advanced undergraduates and first-year graduate students and researchers in theoretical and computational chemistry. It will also be useful to researchers in mathematical physics. It is the first book to systematically explore the application of Lie algebraic methods to simple quantum systems and perturbation theory with an emphasis on symbolic computation. Many exercises complete with solutions are also included. In the first part of the book the basic concepts of Lie algebras are presented in a pedagogical manner, first in the familiar context of angular momentum theory, and then for the important Lie algebras so (2,1), so (4) and so(4,2). Next, a novel feature is the application of the algebraic methods to obtain the energy and wavefunctions of the standard textbook problems of the non-relativistic and relativistic hydrogenic atoms and the harmonic oscillator. This provides an elegant and algebraic alternative to the usual approach using series s