Library of Congress Cataloging in Publieation Data Bohm, Amo, 1936~ Quantum meehanies. (Texts and monographs in physies) Bibliography: p. Includes index. 1. Quantum theory. 1. Title. II. Series QCI74.12.B63 1986 530.1'2 85-4710

No abstract

After a summary of the Jigged Hilbert space formulation of quantum mechanics and a brief statement of its advantages over von Neumann's formulation, a mathematically correct definition of Gamow's exponentially decaying vectors as generalized energy eigenvectors is suggested. It is shown that exponentially decaying vectors are obtained from the S-matrix poles in the lower half of the second sheet and exponentially growing vectors from the S-matrix poles in the upper half of the second sheet. Decaying "state" vectors are defined as functionals over half of the space of physical states and growing "state" vectors are defined as functionals over the other half. On functionals over these subs paces, the dynamical group of time development splits into two semigroups, one for t > 0 and the other for t < O. The generalized basis system connected with the spectrum of the Hamiltonian is transformed into a new basis system in which the exponentially decaying component of the density matrix is separated.