On the Schrödinger equation with a time dependent mass parameter: Nuclear fragmentation theory

Abstract

We study the dynamics of a system with a coordinate-dependent inertia tensorB _ik (x ₁,...,x _n ), in which one of the coordinates is treated classically,x _j →x _j (t), so that the associated mass parameter becomes time-dependent. As a result, the Hamiltonian must contain a pure imaginary term in order that probability be conserved. The nuclear fragmentation theory is an example of such a system. The inertia parameter associated with the mass fragmentation degree of freedom depends on the relative motion coordinate and, hence, on time. The time dependence of the imaginary term is derived from a fully quantum mechanical treatment, by going to the classical limit in the relative motion variable. A connection is made with the closely related situation which arises if one transforms from an inertial system to one which depends non-linearly on the time.