Analytical approach to 1D bound state problems

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...

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Bibliographic Details
Published inThe European physical journal. D, Atomic, molecular, and optical physics Vol. 66; no. 8
Main Authors Šindelka, M., Eleuch, H., Rostovtsev, Y. V.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.08.2012
EDP Sciences
Subjects
Applications of Nonlinear Dynamics and Chaos Theory
Atomic
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Molecular
Optical and Plasma Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Information Technology
Quantum mechanics
Quantum Physics
Regular Article
Solutions of wave equations: bound states
Spectroscopy/Spectrometry
Spintronics
Molecular Physics and Chemical Physics
Energy levels
Bound state
Analytical method
Theoretical study
Quantization
Schroedinger equation
Wave functions
One-dimensional systems
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Summary: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.
ISSN:1434-6060
1434-6079
DOI:10.1140/epjd/e2012-30244-8