17
Laguerre Polynomials
Abstract
Topics of this chapter are the generalized or associated Laguerre polynomials
in the complex domain and its generalization to non-integer degrees via confluent hyperspherical functions. Laguerre polynomials play an important role in
quantum dynamics, e.g., in solving the radial Schrödinger equation for Coulomb
potentials. Code for evaluating Laguerre polynomials, respectively, functions, the
nodes of the polynomials, and the radial wave function can be downloaded. The
Laguerre polynomials are orthogonal polynomials, thus additional methods are
available.
Topics of this chapter are the generalized or associated Laguerre polynomials.
Laguerre polynomials play an important role in quantum dynamics, e.g., in solving
the radial Schrödinger equation for Coulomb potentials. In addition, Laguerre
meshes, based on the roots of the generalized Laguerre polynomials, are used in
approximation techniques.
Function Overview
The SPECFUNPHYS class laguerrepoly supports the evaluation of the polynomial coefficients and the SPECFUNPHYS class laguerrex returns the polynomial
values directly. The SPECFUNPHYS function laguerrezero returns the roots
of the corresponding Laguerre polynomial and Hrad allows to compute the radial
wave function for Coulomb-like potentials.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_17
211
Laguerre Polynomials
Abstract
Topics of this chapter are the generalized or associated Laguerre polynomials
in the complex domain and its generalization to non-integer degrees via confluent hyperspherical functions. Laguerre polynomials play an important role in
quantum dynamics, e.g., in solving the radial Schrödinger equation for Coulomb
potentials. Code for evaluating Laguerre polynomials, respectively, functions, the
nodes of the polynomials, and the radial wave function can be downloaded. The
Laguerre polynomials are orthogonal polynomials, thus additional methods are
available.
Topics of this chapter are the generalized or associated Laguerre polynomials.
Laguerre polynomials play an important role in quantum dynamics, e.g., in solving
the radial Schrödinger equation for Coulomb potentials. In addition, Laguerre
meshes, based on the roots of the generalized Laguerre polynomials, are used in
approximation techniques.
Function Overview
The SPECFUNPHYS class laguerrepoly supports the evaluation of the polynomial coefficients and the SPECFUNPHYS class laguerrex returns the polynomial
values directly. The SPECFUNPHYS function laguerrezero returns the roots
of the corresponding Laguerre polynomial and Hrad allows to compute the radial
wave function for Coulomb-like potentials.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
W. Schweizer, Special Functions in Physics with MATLAB,
https://doi.org/10.1007/978-3-030-64232-7_17
211