Let
jMN (r,j) be the wave function
of the Two-Dimensional Harmonic Oscillator (2-DHO)
in polar coordinates with natural units h = 1
and Mass = 1, which can be expressed in its radial
and angular parts as (Wallace, 1984): and
denoting the associated Laguerre polynomials (Abramowitz
and Stegun, 1972).
Here
the ladder operators , for the radial wave function
(Equation 2), are determined such that: employing
only elementary properties of , i.e., to construct without
the use of specific techniques as the factorization
method (Infeld, 1942; Infeld, 1949; Infeld and Hull,
1948; and Infeld and Hull, 1951). |
