An su(1, 1) algebraic method for the hydrogen atom
Por:
Martínez-Y-Romero R.P., Núñez-Yépez H.N., Salas-Brito A.L.
Publicada:
1 ene 2005
Resumen:
An algebraic solution for the hydrogen atom analogous to the one recently proposed to solve the relativistic version of the system is presented. We add to the usual radial description of the problem an additional angular variable and an associated operator which can be considered as part of an su(1, 1) Lie algebra. The operators of the algebra define radial ladder operator relating the eigenfunctions of the system in unit steps of the principal quantum number. We conclude that the radial bound states of the hydrogen atom in our extended configuration space can be regarded as spanning the minimal M representation of the su(1, 1) Lie algebra. The method can also be extended to solve the s-wave Morse problem and the three-dimensional harmonic oscillator. © 2005 IOP Publishing Ltd.
Filiaciones:
Martínez-Y-Romero R.P.:
Facultad de Ciencias, Universidad Nacional Autónoma de México, Apartado Postal 50-542, Mexico City 04510 DF, Mexico
Núñez-Yépez H.N.:
Departamento de Física, Universidad Autónoma Metropolitana Unidad Iztapalapa, Apartado Postal 55-534, CP 09340, Iztapalapa DF, Mexico
Salas-Brito A.L.:
Laboratorio de Sistemas Dinámicos, Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana Unidad Azcapotzalco, Apartado Postal 21-267, CP 04000, Coyoacán DF, Mexico
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