Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates
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...
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todo:paper_10502947_v40_n8_p4215_Fendrik2023-10-03T15:58:51Z Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates Fendrik, A.J. Bernath, M. 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. Fil:Fendrik, A.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Bernath, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10502947_v40_n8_p4215_Fendrik |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Fendrik, A.J. Bernath, M. |
| spellingShingle |
Fendrik, A.J. Bernath, M. Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| author_facet |
Fendrik, A.J. Bernath, M. |
| author_sort |
Fendrik, A.J. |
| title |
Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| title_short |
Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| title_full |
Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| title_fullStr |
Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| title_full_unstemmed |
Classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| title_sort |
classical and quantum description of the two-dimensional simple harmonic oscillator in elliptic coordinates |
| url |
http://hdl.handle.net/20.500.12110/paper_10502947_v40_n8_p4215_Fendrik |
| work_keys_str_mv |
AT fendrikaj classicalandquantumdescriptionofthetwodimensionalsimpleharmonicoscillatorinellipticcoordinates AT bernathm classicalandquantumdescriptionofthetwodimensionalsimpleharmonicoscillatorinellipticcoordinates |
| _version_ |
1807314609341726720 |