Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

Christian Ringhofer, M. Nedjalkov, H. Kosinas, S. Selberherr

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.

Original languageEnglish (US)
Pages (from-to)1933-1953
Number of pages21
JournalSIAM Journal on Applied Mathematics
Issue number6
StatePublished - 2004


  • Asymptotic analysis
  • Boltzmann equation
  • Fermi's golden rule
  • Levinson equation
  • Quantum mechanics
  • Wigner functions

ASJC Scopus subject areas

  • Applied Mathematics


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