For example , the quantum harmonic oscillator is ideally expanded in Hermite polynomials , and Jacobi - polynomials can be used to define the associated Legendre functions typically appearing in rotational problems .
Such polynomials occur naturally in several standard problems .
The quantum harmonic oscillator is ideally expanded in Hermite polynomials , and Jacobi - polynomials can be used to define the associated Legendre functions typically appearing in rotational problems .
Such polynomials occur naturally in several standard problems .