Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials. (English) Zbl 0877.33005
Summary: The information entropy is explicitly obtained for the harmonic oscillator and the hydrogen atom (Coulomb potential) in \(D\) dimensions \((D=1,2,3)\). It is shown how these entropies are related to entropies involving classical orthogonal polynomials and the physical interpretation of this information entropy is given.
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 33C55 | Spherical harmonics |
| 94A17 | Measures of information, entropy |
| 81V45 | Atomic physics |
