RT info:eu-repo/semantics/article
T1 Superintegrability of the Fock-Darwin system
A1 Drigo Filho, Elso
A1 Kuru, Sengul
A1 Negro Vadillo, Francisco Javier
A1 Nieto Calzada, Luis Miguel
AB The Fock-Darwin system is analysed from the point of view of its symmetry properties in thequantum and classical frameworks. The quantum Fock-Darwin system is known to have twosets of ladder operators, a fact which guarantees its solvability. We show that for rationalvalues of the quotient of two relevant frequencies, this system is superintegrable, the quantumsymmetries being responsible for the degeneracy of the energy levels. These symmetries areof higher order and close a polynomial algebra. In the classical case, the ladder operators arereplaced by ladder functions and the symmetries by constants of motion. We also prove thatthe rational classical system is superintegrable and its trajectories are closed. The constantsof motion are also generators of symmetry transformations in the phase space that have beenintegrated for some special cases. These transformations connect different trajectories withthe same energy. The coherent states of the quantum superintegrable system are found andthey reproduce the closed trajectories of the classical one.
PB Elsevier
SN 0003-4916
YR 2017
FD 2017
LK http://uvadoc.uva.es/handle/10324/23457
UL http://uvadoc.uva.es/handle/10324/23457
LA eng
NO http://dx.doi.org/10.1016/j.aop.2017.05.003
NO Física Teórica, Atómica y Óptica
DS UVaDOC
RD 22-nov-2024