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Application of the higher order finite-element method to one-dimensional Schrödinger equation

✍ Scribed by Toshiyasu Kimura; Nobuyuki Sato; Suehiro Iwata

Publisher
John Wiley and Sons
Year
1988
Tongue
English
Weight
651 KB
Volume
9
Category
Article
ISSN
0192-8651

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✦ Synopsis

The accuracy and applicability of the finite-element method of the higher order interpolation functions to the one-dimensional Schrodinger equation were examined. When the fifth-order Lagrange and Hermite interpolation functions were used as the basis functions, practically exact solutions were obtained for all eigenvalues of several model potential energy functions. It was demonstrated that the appropriate analytical integration over the potential energy function within each element is important in the matrix element evaluation. The accuracy of the method was examined for the potential functions with a double minimum, which has a large classically forbidden region. The method was also applied to evaluate the Franck-Condon factors of the transitions between the 1 '2; and 2 'Z: states of Naz; the latter state having a double minimum in its potential energy function.

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