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
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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
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Año: | 1989
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Volumen: | 40
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Número: | 8
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Página de inicio: | 4215
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Página de fin: | 4223
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DOI: |
http://dx.doi.org/10.1103/PhysRevA.40.4215 |
Título revista: | Physical Review A
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ISSN: | 10502947
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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