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JWKB method as an exact technique
Author(s) -
Shen Hujun,
Silverstone Harris J.
Publication year - 2004
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/qua.20029
Subject(s) - eigenvalues and eigenvectors , divergence (linguistics) , convergence (economics) , mathematics , simple (philosophy) , series (stratigraphy) , boundary value problem , quantum , schrödinger equation , boundary (topology) , mathematical physics , mathematical analysis , pure mathematics , physics , quantum mechanics , paleontology , philosophy , linguistics , epistemology , economics , biology , economic growth
The JWKB method involves divergent asymptotic expansions in powers of ħ. Borel summability turns divergence into convergence, leading to exact solutions of the Schrödinger equation. The formulas that connect real solutions across linear turning points, where the terms of the expansion are singular, are complex but nonunidirectional. A series of basic problems constructed from linear potentials—for which the JWKB solutions are simple, in which the boundary conditions and physics differ, but for which the turning points are the same—is used to demonstrate the nondirectionality of the turning points and how “Borel sum approximants” lead to exact energy eigenvalues. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004