Eigenvalues and eigenfunctions of the anharmonic oscillator V(x, y) = x
2
y
2

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

Abstracts

EN

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential V(x, y) = x
2
y
2 by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it

Keywords

EN

Anharmonic oscillator; discrete spectrum; point-group symmetry; Rayleigh-Ritz method; connected-moments expansion

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 7
• Pages: 499-502

Dates

published

1 - 7 - 2014

online

21 - 6 - 2014

Contributors

author

Francisco Fernández

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

author

Javier Garcia

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

References

• [1] C. M. Bender, G. V. Dunne, P. N. Meisinger, and M. Simsek, Phys. Lett. A 281, 311 (2001) http://dx.doi.org/10.1016/S0375-9601(01)00146-3[Crossref]
• [2] B. Simon, Ann. Phys. 146, 209 (1983) http://dx.doi.org/10.1016/0003-4916(83)90057-X[Crossref]
• [3] P. Amore and F. M. Fernández, Phys. Scr. 80, 055002 (2009) http://dx.doi.org/10.1088/0031-8949/80/05/055002[Crossref]
• [4] J. Cioslowski, Chem. Phys. Lett. 136, 515 (1987) http://dx.doi.org/10.1016/0009-2614(87)80509-2[Crossref]
• [5] P. Knowles, Chem. Phys. Lett. 134, 512 (1987) http://dx.doi.org/10.1016/0009-2614(87)87184-1[Crossref]
• [6] R. A. Pullen and A. R. Edmonds, J. Phys. A 14, L477 (1981)
• [7] F. A. Cotton, Chemical Applications of Group Theory, Third ed. (John Wiley & Sons, New York, 1990)
• [8] M. Tinkham, Group Theory and Quantum Mechanics (McGraw-Hill Book Company, New York, 1964)

Identifiers

DOI

10.2478/s11534-014-0474-7