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Bessel basis with applications: N ‐dimensional isotropic polynomial oscillators
Author(s) -
Taşeli H.,
Zafer A.
Publication year - 1997
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(1997)63:5<935::aid-qua4>3.0.co;2-x
Subject(s) - bessel function , eigenvalues and eigenvectors , isotropy , polynomial , series (stratigraphy) , anharmonicity , space (punctuation) , mathematical analysis , fourier series , bessel polynomials , mathematics , spectral line , physics , quantum mechanics , orthogonal polynomials , paleontology , linguistics , philosophy , macdonald polynomials , biology , difference polynomials
The efficient technique of expanding the wave function into a Fourier–Bessel series to solve the radial Schrödinger equation with polynomial potentials, $V(r)=\sum_{i=1}^{K} v_{2i} r^{2i}$ , in two dimensions is extended to N ‐dimensional space. It is shown that the spectra of two‐ and three‐dimensional oscillators cover the spectra of the corresponding N ‐dimensional problems for N . Extremely accurate numerical results are presented for illustrative purposes. The connection between the eigenvalues of the general anharmonic oscillators and the confinement potentials of the form $V(r)=-Z/r+\sum_{i=1}^{K-1} c_i r^i$ is also discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 935–947, 1997