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 -