QUANTUM MOTION OVER A FINITE ONE-DIMENSIONAL DOMAIN - WITH AND WITHOUT DISSIPATION

Quantum motion of a single particle over a finite one-dimensional spat ial domain is considered for the generalized four parameter infinity o f boundary conditions (GBC) of Carreau ct al [1]. The boundary conditi ons permit complex eigenfunctions with nonzero current for discrete st ates. Explicit expressions are obtained for the eigenvalues and eigenf unctions. It is shown that these states go over to plane waves in the limit of the spatial domain becoming very large. Dissipation is introd uced through Schrodinger-Langevin (SL) equation. The space and time pa rts of the SL equation are separated and the time part is solved exact ly. The space part is converted to nonlinear ordinary differential equ ation. This is solved perturbatively consistent with the GBC. Various special cases are considered for illustrative purposes.