Rayleigh-Ritz variational method with suitable asymptotic behaviour

• Authors: Francisco Fernández , Javier Garcia
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

Rayleigh-Ritz method; asymptotic behaviour; anharmonic oscillators; rate of convergence; orthogonal polynomial projection quantization

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 8
• Pages: 554-558

Dates

published

1 - 8 - 2014

online

20 - 7 - 2014

Contributors

author

Francisco Fernández

• INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica Diag, 113 y 64 (S/N), Sucursal 4, Casilla de Correo, 16 1900, La Plata, Argentina

author

Javier Garcia

• INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica Diag, 113 y 64 (S/N), Sucursal 4, Casilla de Correo, 16 1900, La Plata, Argentina

References

• [1] C. N. Handy, D. Vrinceanu, J. Phys. A 46, 135202 (2013) http://dx.doi.org/10.1088/1751-8113/46/13/135202[Crossref]
• [2] F. L. Pilar, Elementary Quantum Chemistry (McGraw-Hill, New York, 1968)
• [3] F. M. Fernández, Cent. Eur. J. Phys. 11, 470 (2013). arXiv:1204.0229 [math-ph] http://dx.doi.org/10.2478/s11534-013-0198-0[Crossref]
• [4] F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 39, 1605 (1989) http://dx.doi.org/10.1103/PhysRevA.39.1605[Crossref]
• [5] F. M. Fernández, Q. Ma, R. H. Tipping, Phys. Rev. A 40, 6149 (1989) http://dx.doi.org/10.1103/PhysRevA.40.6149[Crossref]

Identifiers

DOI

10.2478/s11534-014-0477-4