  Transient simulations of a resonant tunneling diode oscillator are presented.
The semiconductor model for the diode consists of a set of time-dependent
Schr\"odinger equations coupled to the Poisson equation for the electric
potential. The one-dimensional Schr\"odinger equations are discretized by the
finite-difference Crank-Nicolson scheme using memory-type transparent boundary
conditions which model the injection of electrons from the reservoirs. This
scheme is unconditionally stable and reflection-free at the boundary. An
efficient recursive algorithm due to Arnold, Ehrhardt, and Sofronov is used to
implement the transparent boundary conditions, enabling simulations which
involve a very large number of time steps. Special care has been taken to
provide a discretization of the boundary data which is completely compatible
with the underlying finite-difference scheme. The transient regime between two
stationary states and the self-oscillatory behavior of an oscillator circuit,
containing a resonant tunneling diode, is simulated for the first time.
