TY - JOUR
T1 - Survival probability of a quantum particle in the presence of an absorbing surface
AU - Marchewka, A.
AU - Schuss, Z.
PY - 2001
Y1 - 2001
N2 - 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 an 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 applications are given: the calculation of the absorption current in the slit experiment with a totally absorbing screen, the calculation of the survival probability of a particle between two totally absorbing walls, and the calculation of the survival probability and of the reflection coefficient of a Gaussian wave packet incident on a totally absorbing wall. The survival probability of a one-dimensional particle between two totally absorbing walls exhibits decay with beats.
AB - 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 an 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 applications are given: the calculation of the absorption current in the slit experiment with a totally absorbing screen, the calculation of the survival probability of a particle between two totally absorbing walls, and the calculation of the survival probability and of the reflection coefficient of a Gaussian wave packet incident on a totally absorbing wall. The survival probability of a one-dimensional particle between two totally absorbing walls exhibits decay with beats.
UR - http://www.scopus.com/inward/record.url?scp=33646203684&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.63.032108
DO - 10.1103/PhysRevA.63.032108
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AN - SCOPUS:33646203684
SN - 1050-2947
VL - 63
SP - 1
EP - 10
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 3
M1 - 032108
ER -