TY - JOUR

T1 - The case of escape probability as linear in short time

AU - Marchewka, A.

AU - Schuss, Z.

N1 - Publisher Copyright:
© 2017 Elsevier B.V.

PY - 2018/2/20

Y1 - 2018/2/20

N2 - We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.

AB - We derive rigorously the short-time escape probability of a quantum particle from its compactly supported initial state, which has a discontinuous derivative at the boundary of the support. We show that this probability is linear in time, which seems to be a new result. The novelty of our calculation is the inclusion of the boundary layer of the propagated wave function formed outside the initial support. This result has applications to the decay law of the particle, to the Zeno behaviour, quantum absorption, time of arrival, quantum measurements, and more.

KW - Boundary layer

KW - Escape probability

KW - Linear in time

KW - Quadratic in time

KW - Short time

UR - http://www.scopus.com/inward/record.url?scp=85039156874&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2017.12.039

DO - 10.1016/j.physleta.2017.12.039

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AN - SCOPUS:85039156874

SN - 0375-9601

VL - 382

SP - 461

EP - 463

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 7

ER -