Survival probability of a quantum particle in the presence of an absorbingsurface - art. no. 032108

We propose a formulation of an absorbing boundary for a quantum particle. T he formulation is based on a Feynman-type integral over trajectories that a re confined by an absorbing boundary. Trajectories that reach the absorbing wall are instantaneously terminated and their probability is discounted fr om the population of the surviving trajectories. This gives rise to a unidi rectional absorption current at the boundary. We calculate the survival pro bability as a function of time. Several applications are given: the calcula tion of the absorption current in the slit experiment with a totally absorb ing screen, the calculation of the survival probability of a particle betwe en two totally absorbing walls, and the calculation of the survival probabi lity and of the reflection coefficient of a Gaussian wave packet incident o n a totally absorbing wall. The survival probability of a one-dimensional p article between two totally absorbing walls exhibits decay with beats.