SciELO - Scientific Electronic Library Online

vol.50 número6CIE-XYZ fitting by multispectral images and mean square error minimization with a linear interpolation functionSubband structure comparison between n- and p-type double delta-doped GaAs quantum wells índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • No hay artículos similaresSimilares en SciELO


Revista mexicana de física

versión impresa ISSN 0035-001X


TORRES DEL CASTILLO, G.F.  y  VELAZQUEZ QUESADA, M.P.. Symplectic structures and dynamical symmetry groups. Rev. mex. fis. [online]. 2004, vol.50, n.6, pp.608-613. ISSN 0035-001X.

Apart from the total energy, the two-dimensional isotropic harmonic oscillator possesses three independent constants of motion which, with the standard symplectic structure, generates a dynamical symmetry group isomorphic to SU(2). We show that, by suitably redefining the symplectic structure, any of these three constants of motion can be used as a Hamiltonian, and that the remaining two, together with the total energy, generate a dynamical symmetry group isomorphic to SU(1,1). We also show that the standard energy levels of the quantum two-dimensional isotropic harmonic oscillator and their degeneracies are obtained making use of the appropriate representations of SU(1,1), provided that the canonical commutation relations are modified according to the new symplectic structure. Whereas in classical mechanics the different symplectic structures lead to equivalent formulations of the equations of motion, in quantum mechanics the modifications of the commutation relations should be accompanied by modifications in the interpretation of the formalism in order to obtain results equivalent to those found with the common relations.

Palabras llave : Dynamical symmetry groups; symplectic structures; quantization.

        · resumen en Español     · texto en Inglés     · Inglés ( pdf )


Creative Commons License Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons