Short-time quantum dynamics of sharp boundaries potentials

Er'El Granot, Avi Marchewka

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Despite the high prevalence of singular potential in general, and rectangular potentials in particular, in applied scattering models, to date little is known about their short time effects. The reason is that singular potentials cause a mixture of complicated local as well as non-local effects. The object of this work is to derive a generic method to calculate analytically the short-time impact of any singular potential. In this paper it is shown that the scattering of a smooth wavefunction on a singular potential is totally equivalent, in the short-time regime, to the free propagation of a singular wavefunction. However, the latter problem was totally addressed analytically in Ref. [7]. Therefore, this equivalency can be utilized in solving analytically the short time dynamics of any smooth wavefunction at the presence of a singular potentials. In particular, with this method the short-time dynamics of any problem where a sharp boundaries potential (e.g., a rectangular barrier) is turned on instantaneously can easily be solved analytically.

Original languageEnglish
Pages (from-to)62-68
Number of pages7
JournalPhysica B: Condensed Matter
StatePublished - 15 Feb 2015


  • Barrier
  • Quantum currents
  • Short-time
  • Tunneling


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