https://doi.org/10.1140/epjd/e2012-30244-8
Regular Article
Analytical approach to 1D bound state problems
1 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
2 Department of Physics, University of North Texas, 1155 Union Circle 311427, TX 76203-5017 Denton, USA
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e-mail: milan@pks.mpg.de
Received: 13 April 2012
Received in final form: 17 June 2012
Published online: 30 August 2012
Using a recently developed new analytic approach to solution of the 1D Schrödinger equation [Eleuch et al., Europhys. Lett. 89, 50004 (2010)], we derive a quantization rule determining the positions of bound state energy levels in an arbitrary potential. The obtained quantization formula is applied to a simple model problem and is found to be superior to the well known Bohr-Sommerfeld (JWKB) quantization rule. Contrary to the JWKB prescription, our new formula contains extra contributions arising from the classically forbidden regions. The corresponding analytic wavefunctions are smooth even at the classical turning points.
Key words: Molecular Physics and Chemical Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012
