Transition Decomposition of Quantum Mechanical Evolution

Y. Strauss, J. Silman, S. Machnes, L. P. Horwitz

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We show that the existence of the family of self-adjoint Lyapunov operators introduced in Strauss (J. Math. Phys. 51:022104, 2010) allows for the decomposition of the state of a quantum mechanical system into two parts: A backward asymptotic component, which is asymptotic to the state of the system in the limit t→-∞ and vanishes at t→∞, and a forward asymptotic component, which is asymptotic to the state of the system in the limit t→∞ and vanishes at t→-∞. We demonstrate the usefulness of this decomposition for the description of resonance phenomena by considering the resonance scattering of a particle off a square barrier potential. We show that the evolution of the backward asymptotic component captures the behavior of the resonance. In particular, it provides a spatial probability distribution for the resonance and exhibits its typical decay law.

Original languageEnglish
Pages (from-to)2179-2190
Number of pages12
JournalInternational Journal of Theoretical Physics
Volume50
Issue number7
DOIs
StatePublished - 1 Jul 2011
Externally publishedYes

Keywords

  • Lyapunov operator
  • Resonance
  • Semigroup decomposition
  • Transition decomposition

ASJC Scopus subject areas

  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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