Several interesting behaviors of resonant tunneling diodes (RTDs) are investigated through numerical simulation: high frequency self-oscillations, strong intrinsic hysteresis, and pronounced static bistability. Each of these behaviors has been observed experimentally in RTDs, but the measured effects have been slower (oscillations), weaker (hysteresis, bistability), or required external inductance to occur (oscillations, hysteresis). These simulations indicate that the effects occur strongly and intrinsically in an RTD when a narrow energy band in the emitter aligns just below a quantized energy state in the quantum well. Quantum system models and available computation power have only recently developed to a point where the necessary physical effects (inelastic scattering, self-consistency, and transient operation) can be properly included to simulate these behaviors in a quantum device. A 1-D Wigner function model is used for transient, self-consistent RTD simulations including inelastic scattering. One-dimensional transfer-matrix calculations are used to locate quantized energy levels. The physics behind the intrinsic oscillations, hysteresis and bistability are described for the simulated RTD. Simulation results are also presented for double-well RTD structures in an attempt to enhance these effects.