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Perturbation expansions, symanzik scaling, and padé‐type approximants: The anharmonic oscillator problem
Author(s) -
Chandra A. K.,
Bhattacharyya K.
Publication year - 1993
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.560450303
Subject(s) - anharmonicity , quartic function , scaling , virial theorem , taylor series , observable , perturbation theory (quantum mechanics) , mathematical physics , physics , padé approximant , quantum mechanics , power series , mathematics , mathematical analysis , pure mathematics , geometry , galaxy
The problem of representing an observable F(z) in the Padé scheme from its formal perturbative (Taylor) expansion in z is considered. It is demonstrated how the representation could be improved by incorporating in a simple manner, in the course of constructing such approximants, the knowledge of asymptotic ( z → ∞) power‐law behavior of F(z) . Comparison with the usual approximants is made with a thorough numerical survey on error estimates and variations of error with z , input information, and quantum number. Spectacular performance of the new strategy is exemplified. Test calculations chiefly involve various properties of the first five eigenenergy states of the quartic anharmonic oscillator system. A few consistency requirements, including the virial theorem, are also studied. © 1993 John Wiley & Sons, Inc.