Memoirs of the American Mathematical Society 1994; 130 pp; softcover Volume: 111 ISBN10: 0821826050 ISBN13: 9780821826058 List Price: US$42 Individual Members: US$25.20 Institutional Members: US$33.60 Order Code: MEMO/111/536
 This largely selfcontained book provides a thorough discussion of the mathematics of molecular dynamics and fills a gap in the theoretical knowledge of the subject. Most knowledge of molecular propagation is derived from the timedependent BornOppenheimer approximation. This approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. Hagedorn classifies generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. He then extends the timedependent BornOppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing. Readership Mathematical physicists interested in quantum mechanics; molecular physicists; theoretical chemists. Table of Contents  Introduction
 Generic minimal multiplicity quantum eigenvalue crossings
 Technical preliminaries
 BornOppenheimer propagation away from crossings
 Codimension 1 crossings
 Codimension 2 crossings
 Codimension 3 crossings
 Codimension 5 crossings
 References
