laguerreGauss

laguerreGauss (p, m, r)

The LaguerreGauss function returns the normalized product of the associated Laguerre polynomials and a Gaussian. This function is typically encountered in solutions to physical problems where it represents the radial solution with an additional factor exp(imφ) which is not included in this case. The laguerreGauss is given by

$$\displaystyle U_{p m}(r)=\sqrt{\frac{2 p!}{\pi(m+p)!}}(r \sqrt{2})^{m} L_{p}^{m}\left(2 r^{2}\right) \exp \left(-r^{2}\right) .$$

See Also

laguerre, laguerreA, hermiteGauss