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Doubly uniform semiclassical quantization formula for resonances
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-0149-341X
2009 (English)In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 53, no 3, 283-288 p.Article in journal (Refereed) Published
Abstract [en]

The radial Schrodinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point. Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of 'exact' numerical computations. The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.

Place, publisher, year, edition, pages
2009. Vol. 53, no 3, 283-288 p.
Keyword [en]
complex, states
URN: urn:nbn:se:kth:diva-18479DOI: 10.1140/epjd/e2009-00140-7ISI: 000266566600003ScopusID: 2-s2.0-67349167677OAI: diva2:336526
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-12Bibliographically approved

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