The case of escape probability as linear in short time

A. Marchewka*, Z. Schuss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)461-463
Number of pages3
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number7
StatePublished - 20 Feb 2018


  • Boundary layer
  • Escape probability
  • Linear in time
  • Quadratic in time
  • Short time


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