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Wentzel-Kramers-Brillouin method in the Bargmann representationIt is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.
Document ID
19900032525
Document Type
Reprint (Version printed in journal)
Authors
Voros, A. (California, University Santa Barbara; CEA, Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette, France)
Date Acquired
August 14, 2013
Publication Date
December 15, 1989
Publication Information
Publication: Physical Review A - General Physics, 3rd Series
Volume: 40
ISSN: 0556-2791
Subject Category
PHYSICS (GENERAL)
Funding Number(s)
CONTRACT_GRANT: NSF PHY-82-17853
Distribution Limits
Public
Copyright
Other