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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 20, 2014

Rayleigh-Ritz variational method with suitable asymptotic behaviour

Francisco Fernández EMAIL logo and Javier Garcia
From the journal Open Physics

Abstract

This paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.

[1] C. N. Handy, D. Vrinceanu, J. Phys. A 46, 135202 (2013) http://dx.doi.org/10.1088/1751-8113/46/13/13520210.1088/1751-8113/46/13/135202Search in Google Scholar

[2] F. L. Pilar, Elementary Quantum Chemistry (McGraw-Hill, New York, 1968) Search in Google Scholar

[3] F. M. Fernández, Cent. Eur. J. Phys. 11, 470 (2013). arXiv:1204.0229 [math-ph] http://dx.doi.org/10.2478/s11534-013-0198-010.2478/s11534-013-0198-0Search in Google Scholar

[4] F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 39, 1605 (1989) http://dx.doi.org/10.1103/PhysRevA.39.160510.1103/PhysRevA.39.1605Search in Google Scholar PubMed

[5] F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 40, 6149 (1989) http://dx.doi.org/10.1103/PhysRevA.40.614910.1103/PhysRevA.40.6149Search in Google Scholar

Published Online: 2014-7-20
Published in Print: 2014-8-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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