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Abstract:

The Schrödinger equation for the two-dimensional simple harmonic oscillator is solved using elliptic coordinates where it is separable. The separability of the problem in such coordinates is independent of the selection of the focal distance. The solutions are labeled by the total number of quanta N and by a set of characteristic values b corresponding to the eigenvalues of an observable B^, which does not commute with L^, the total angular momentum or H^x, the energy associated with the x degree of freedom. The well-known quantum energies as well as the characteristic values are obtained by imposing physical polynomial solutions. © 1989 The American Physical Society.

Registro:

Documento: Artículo
Título:Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates
Autor:Fendrik, A.J.; Bernath, M.
Filiación:Departamento de Física, Facultad de Ciencias Exactas Y Naturales, Ciudad Universitaria, 1428, Buenos Aires, Argentina
Departamento de Física, Comision Nacional de Energía Atmica, Avenida del Libertador 8250, 1429, Buenos Aires, Argentina
Año:1989
Volumen:40
Número:8
Página de inicio:4215
Página de fin:4223
DOI: http://dx.doi.org/10.1103/PhysRevA.40.4215
Título revista:Physical Review A
ISSN:10502947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10502947_v40_n8_p4215_Fendrik

Referencias:

  • Bracken, A.J., Leemon, H.I., A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states (1981) Journal of Mathematical Physics, 22, p. 719
  • Bracken, A.J., McAnally, D.S., Odundun, O.A., (1987) J. Math. Phys., 28, p. 397
  • Boyer, C.P., Kalnis, E.G., Miller, H., Jr., Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials (1975) Journal of Mathematical Physics, 16, p. 512
  • Ayant, Y., Arvieu, R., (1987) J. Phys. A, 20, p. 397
  • Arvieu, R., Ayant, Y., (1987) J. Phys. A, 20, p. 1115
  • Traiber, A.J.S., Fendrik, A.J., Bernath, M., (1989) J. Phys. A: Math. Gen., 22, p. L365
  • Berry, M.V., (1981) Eur. J. Phys., 2, p. 91
  • Stratton, J.A., (1941) Electromagnetic Theory, , McGraw-Hill, New York

Citas:

---------- APA ----------
Fendrik, A.J. & Bernath, M. (1989) . Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates. Physical Review A, 40(8), 4215-4223.
http://dx.doi.org/10.1103/PhysRevA.40.4215
---------- CHICAGO ----------
Fendrik, A.J., Bernath, M. "Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates" . Physical Review A 40, no. 8 (1989) : 4215-4223.
http://dx.doi.org/10.1103/PhysRevA.40.4215
---------- MLA ----------
Fendrik, A.J., Bernath, M. "Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates" . Physical Review A, vol. 40, no. 8, 1989, pp. 4215-4223.
http://dx.doi.org/10.1103/PhysRevA.40.4215
---------- VANCOUVER ----------
Fendrik, A.J., Bernath, M. Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates. 1989;40(8):4215-4223.
http://dx.doi.org/10.1103/PhysRevA.40.4215