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On the exact solution of the Schrödinger equation with a quartic anharmonicity
Author(s) -
Taşeli H.
Publication year - 1996
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(1996)57:1<63::aid-qua7>3.0.co;2-x
Subject(s) - anharmonicity , quartic function , eigenfunction , exact solutions in general relativity , power series , series (stratigraphy) , harmonic oscillator , schrödinger equation , mathematical analysis , function (biology) , wave function , harmonic , elementary function , mathematics , physics , mathematical physics , quantum mechanics , eigenvalues and eigenvectors , pure mathematics , paleontology , evolutionary biology , biology
A new version of solutions in the form of an exponentially weighted power series is constructed for the two‐dimensional circularly symmetric quartic oscillators, which reflects successfully the desired properties of the exact wave function. The regular series part is shown to be the solution of a transformed equation. The transformed equation is applicable to the one‐dimensional problem as well. Moreover, the exact closed‐form eigenfunctions of the harmonic oscillator can be reproduced as a special case of the present wave function. © 1996 John Wiley & Sons, Inc.