Validity of the adiabatic approximation in quantum mechanics

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.044102· OSTI ID:21020842

MacKenzie, R; Morin-Duchesne, A; Paquette, H; Pinel, J ^[1]

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1. Groupe de physique des particules, Universite de Montreal, Case Postale 6128, Succursale Centre-ville, Montreal, Quebec, H3C 3J7 (Canada)

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the 'standard criterion' for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic theorem and the adiabatic approximation, two quite different, although closely related, ideas.

• OSTI ID: 21020842
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADIABATIC APPROXIMATION
EVOLUTION
HAMILTONIANS
QUANTUM MECHANICS
RELIABILITY
SCHROEDINGER EQUATION