  We propose a formulation of an absorbing boundary for a quantum particle. The
formulation is based on a Feynman-type integral over trajectories that are
confined by the absorbing boundary. Trajectories that reach the absorbing wall
are instantaneously terminated and their probability is discounted from the
population of the surviving trajectories. This gives rise to a unidirectional
absorption current at the boundary. We calculate the survival probability as a
function of time. Several modes of absorption are derived from our formalism:
total absorption, absorption that depends on energy levels, and absorption of
non-interacting particles. Several applications are given: the slit experiment
with an absorbing screen and with absorbing lateral walls, and one dimensional
particle between two absorbing walls. The survival probability of a particle
between absorbing walls exhibits decay with beats.
