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Physica A Statistical Mechanics and its Applications

General properties of gausson-conserving descriptions of quantal damped motion

E. Susana Hernández, B. Rémaud

Published Jan 1, 1981• 42 citations
Publisher
DOI
10.1016/0378-4371(81)90066-2

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The phenomenological optical potential model of nuclear physics is studied to determine how it corresponds to the classical damped motion. Using the Ehrenfest theorem, it is shown that (1) the usual correspondence between the classical and quantal descriptions does not hold in the presence of optical potentials, (2) the number of degrees of freedom for the motion of a particle is twice the dimension of the space in which it is constrained to move, and (3) the canonical and the mechanical momenta are not the same. An example of an optical potential which has a classical analog is studied in some detail, and it is shown that a consistent solution can be found if a set of coordinates equal in number to the degrees of freedom is chosen for the description of the motion. A new Hamiltonian formulation for the linearly damped motion is obtained which is similar to the Hamiltonian proposed by Feshbach and Tikochinsky.
The authors provide a framework for the study of a quantal time-dependent oscillator in the presence of a loss mechanism. Previous approaches to partial aspects of the problem are analysed and cast into a unified global picture. Several alternative descriptions of the situation are analysed and it is shown that the proper generalisation of the Hamiltonian formulation by Kostin (1975) is adequate for the case under consideration. Applications to a number of problems in which the mass of the oscillator is a given function of time are presented, including cases in which the mass becomes infinite.