Perturbative approach to the adiabatic approximation

Journal Article · Sat Apr 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.0· OSTI ID:20787064

MacKenzie, R ^[1]; Marcotte, E; Paquette, H ^[1]

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1. Physique des Particules, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, QC H3C 3J7 (Canada)

A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous eigenstate of the initial Hamiltonian is written as a power series which has a straightforward diagrammatic representation. Each term of the series corresponds to a sequence of ''adiabatic'' evolutions, during which the system remains in an instantaneous eigenstate of the Hamiltonian, punctuated by transitions from one state to another. The first term of this series is the standard adiabatic evolution, the next is the well known first correction to it, and subsequent terms can be written down essentially by inspection. Although the final result is perhaps not terribly surprising, it seems to not be widely known, and the interpretation is new, as far as we know. Application of the method to the adiabatic approximation is given, and some discussion of the validity of this approximation is presented.

• OSTI ID: 20787064
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 73; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ADIABATIC APPROXIMATION
CORRECTIONS
EIGENFUNCTIONS
EIGENSTATES
EIGENVALUES
HAMILTONIANS
PERTURBATION THEORY
POWER SERIES
QUANTUM MECHANICS
TIME DEPENDENCE