An approach to ladder operators for the two-dimensional harmonic oscillator

• López-Bonilla, José ^[1] ; Cruz-Beltrán, L. ^[1]
  1. [1] Instituto Politécnico Nacional

     Instituto Politécnico Nacional

     México

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 15, Nº. 1, 2008, págs. 97-99
• Idioma: inglés
• DOI: 10.15517/rmta.v15i1.291
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Demostramos que propiedades elementales de polinomios de Laguerre generan operadoresescalera para la funci´on de onda del oscilador radial arm´onico en dos dimensiones.Palabras clave: Oscilador arm´onico, operadores escalera, polinomios de Laguerre.

  • English

    We show that elementary properties of associated Laguerre polynomials generatethe ladder operators for the harmonic oscillator radial wave function in two dimensions.Keywords: Harmonic oscillator, ladder operators, Laguerre polynomials.

• Referencias bibliográficas
  • Wallace, P.R. (1984) Mathematical Analysis of Physical Problems. Dover, New York.
  • Abramowitz, M.; Stegun, I.A. (1972) Handbook of Mathematical Functions. John Wiley and Sons, New York.
  • Infeld, L. (1942) “A generalization of the factorization method of solving eigenvalue problems”, Trans. Canad. Roy. Soc. Ser. III 36: 7–18.
  • Infeld, L.; Hull, T.E. (1948) “The factorization method, hydrogen intensities and related problems”, Phys. Rev. 74: 905–909.
  • Infeld, L. (1949) “The factorization method and its application to differential equations in Theoretical Physics”, Proc. Symp. Appl. Math....
  • Infeld, L.; Hull, T.E. (1951) “The factorization method”, Rev. Mod. Phys. 23: 21–68.
  • López-Bonilla, J. ; Morales, J.; Rosales, M. (1995) “Hypervirial theorem and matrix elements for the Coulomb potential”, Int. J. Quantum...
  • Bautista-Moedano, M.; López Bonilla, J.; Morales, J. (2006) “Matrix elements 〈n2l2 |rk | n1l1〉 for the Coulomb interaction”, Apeiron 13(1):...
  • Gaftoi, V.; López Bonilla, J.; Peña, J.J. (2000) “Ladder operators for the Coulomb potential”, Indian J. Phys. B74: 171–172.
  • Martínez, R.P.; Romero, Y.; Núñez-Yépez, H.N.; Salas-Brito, A.L. (2007) “Algebraic approach to radial ladder operators in the hydrogen...