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HAIT Journal of Science and Engineering A Volume 5, Issues 1-2, pp. 71-92 © 2008 Holon Institute of Technology | |||||
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Accuracy of semiclassics: Comparative analysis of WKB and instanton approaches
Victor A. Benderskii1,2, Evgenii V. Vetoshkin1, and Efim I. Kats2,3,*
1Institute of Problems of Chemical Physics, RAS, | Moscow Region, Chernogolovka 142432, Russia 2Laue-Langevin Institute, F-38042, Grenoble, France 3L.D. Landau Institute for Theoretical Physics, RAS, Moscow 119334, Russia 4Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg, Germany *Corresponding author: kats@ill.fr Received 6 April 2007
| We analyze quantitatively the accuracy of eigenfunction and eigenvalue calculations in the frame work of WKB and instanton semiclassical methods. We show that to estimate the accuracy it is enough to compare two linearly independent (with the same quantum number) solutions to the Schrödinger equations with the potential under study, and with the approximating piecewise smooth potential. The main advantage of the approach is related to the appropriate choice of the approximating potential, providing absolutely convergent majorant series for the solutions. We test our method for a strongly anharmonic one dimensional potential, but the basic ideas inspiring our work and its results can be applied to a large variety of interesting chemical and physical problems which are of relevance to various molecular systems. PACS: 05.45.-a, 72.10.-d
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