Discrete Time and Intrinsic Length in Quantum Mechanics

We consider the possibility that simultaneously time and intrinsic length can be regarded as discrete real parameters. We study the dynamics of the free particle. For both scattering and bound states there are configurations where the energy is bounded from above and from below even for positive wave-function solutions. For the case of continuous evolution we show that the wave equation with a linear scalar coupling describes an oscillator that has built-in hidden supersymmetry.