Keywords
ladder operators
Laguerre polynomials
Oscilador armónico
operadores escalera
polinomios de Laguerre
How to Cite
Abstract
We show that elementary properties of associated Laguerre polynomials generate the ladder operators for the harmonic oscillator radial wave function in two dimensions.
References
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. 28: 58–65.
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 Chem. 53: 3–7.
Bautista-Moedano, M.; López Bonilla, J.; Morales, J. (2006) “Matrix elements 〈n2l2 |rk | n1l1〉 for the Coulomb interaction”, Apeiron 13(1): 34–42.
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 atom”, Int. J. Quantum Chem. 107: 1606–1613.