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.