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oai:uvadoc.uva.es:10324/234572026-03-20T08:24:06Zcom_10324_22154com_10324_954com_10324_894col_10324_22155

2017-06-06T12:33:07Z urn:hdl:10324/23457 Superintegrability of the Fock-Darwin system Drigo Filho, Elso Kuru, Şengül Negro Vadillo, Francisco Javier Nieto Calzada, Luis Miguel The Fock-Darwin system is analysed from the point of view of its symmetry properties in the quantum and classical frameworks. The quantum Fock-Darwin system is known to have two sets of ladder operators, a fact which guarantees its solvability. We show that for rational values of the quotient of two relevant frequencies, this system is superintegrable, the quantum symmetries being responsible for the degeneracy of the energy levels. These symmetries are of higher order and close a polynomial algebra. In the classical case, the ladder operators are replaced by ladder functions and the symmetries by constants of motion. We also prove that the rational classical system is superintegrable and its trajectories are closed. The constants of motion are also generators of symmetry transformations in the phase space that have been integrated for some special cases. These transformations connect different trajectories with the same energy. The coherent states of the quantum superintegrable system are found and they reproduce the closed trajectories of the classical one. 2017-06-06T12:33:07Z 2017-06-06T12:33:07Z 2017 info:eu-repo/semantics/article http://dx.doi.org/10.1016/j.aop.2017.05.003 Annals of Physics, 2017, vol. 383. p. 101-119 0003-4916 http://uvadoc.uva.es/handle/10324/23457 eng info:eu-repo/semantics/openAccess Elsevier