Advertisement

Special Functions of Mathematical Physics

  • Siegmund BrandtEmail author
  • Hans Dieter Dahmen
  • Tilo Stroh
Chapter

Abstract

Discussion of the most important formulae and construction of plots for some functions of mathematical physics relevant to quantum mechanics. These functions are Hermite polynomials, Legendre polynomials and Legendre functions, spherical harmonics, Bessel functions and spherical Bessel functions, Airy functions, and Laguerre polynomials.Directly related to some of these and also dis-cussed are the eigenfunctions of the one-dimensional harmonic oscillator and the radial eigenfunctions of the harmonic oscillator in three dimensions and of the hydrogen atom. From statistics the Gaussian distribution of one and two variables and the error function as well as the binomial and Poisson distributions are described.

Keywords

Bessel Function Spherical Harmonic Polar Diagram Hermite Polynomial Cartesian Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Siegmund Brandt
    • 1
    Email author
  • Hans Dieter Dahmen
    • 1
  • Tilo Stroh
    • 1
  1. 1.Physics DepartmentSiegen UniversitySiegenGermany

Personalised recommendations