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WKB and MAF quantization rules for spatially confined quantum mechanical systems
Author(s) -
Sinha Anjana,
Roychoudhury Rajkumar
Publication year - 1999
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1999)73:6<497::aid-qua4>3.0.co;2-b
Subject(s) - wkb approximation , quartic function , airy function , harmonic oscillator , quantization (signal processing) , eigenvalues and eigenvectors , quantum mechanics , physics , quantum , formalism (music) , anharmonicity , classical mechanics , mathematical physics , mathematics , art , musical , algorithm , pure mathematics , visual arts
A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel–Kramers–Brillouin (WKB) and modified airy function (MAF) methods. To illustrate the working rule, the techniques are applied to three different cases, viz. the confined one‐dimensional harmonic and quartic oscillators and a boxed‐in charged particle subject to an external electric field. The energies thus obtained are compared with those from shifted 1/ N expansion, variational, and other methods, as well as the available exact numerical results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 497–504, 1999