author={Charles F. Dunkl},
  journal={Analysis and Applications},
  • C. Dunkl
  • Published 13 November 2000
  • Mathematics
  • Analysis and Applications
The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis, an analogous strange orthogonality is… 

Inverse momentum expectation values for hydrogenic systems

By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials), one may find expectation values of arbitrary functions of momentum p. In this

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A metastable energy band of electron pairs between the two lowest single-electron bands is found that result from interplay of the electron-Electron Coulomb interaction and the strength of the crystal potential.

Some identities for the generalized Laguerre polynomials

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Electron pairing: from metastable electron pair to bipolaron

Starting from the shell structure in atoms and the significant correlation within electron pairs, we distinguish the exchange-correlation effects between two electrons of opposite spins occupying the

Laguerre semigroup and Dunkl operators

Abstract We construct a two-parameter family of actions ωk,a of the Lie algebra 𝔰𝔩(2,ℝ) by differential–difference operators on ℝN∖{0}. Here k is a multiplicity function for the Dunkl operators,

Exact Wavelets on the Ball

A multiresolution algorithm to perform the flaglet transform rapidly, while capturing all information at each wavelet scale in the minimal number of samples on the ball is introduced, which achieves floating-point precision.

Generalized Kepler problems. I. Without magnetic charges

For each simple euclidean Jordan algebra V of rank ρ and degree δ, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler

External Ellipsoidal Harmonics for the Dunkl-Laplacian ?

The paper introduces external ellipsoidal and external sphero-conal h-harmonics for the Dunkl-Laplacian. These external h-harmonics admit integral representations, and they are connected by a formula

Information and Entanglement Measures in Quantum Systems With Applications to Atomic Physics

This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions



Upper limit of the discrete hydrogen-like wave functions: Expansion in the inverse principal quantum number n−1

We have expanded the Schrodinger hydrogen-like wave functions ψnlm of the discrete spectrum, with respect to the inverse principal quantum number n−1, for fixed values of the quantum numbers l,m. The

Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials

The information entropies of the two-dimensional harmonic oscillator, V(x,y)=1/2λ(x2+y2), and the one-dimensional hydrogen atom, V(x)=−1/|x|, can be expressed by means of some entropy integrals of

Asymptotic Formulas for the Zeros of the Meixner Polynomials

The zeros of the Meixner polynomialmn(x;s,c) are real, distinct, and lie in (0,∞). Let?n,sdenote thesth zero ofmn(n?;s,c), counted from the right; and let?n,sdenote thesth zero ofmn(n?;s,c), counted

Uniform Asymptotic Expansions for Meixner Polynomials

Abstract. Meixner polynomials mn(x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are $j(x;\beta,c) =

Quantum mechanics

Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.

The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac

A system for automatically reading symbols, preferably figures, which are hand-written on an information carrier in an arrangement of squares provided on the information carrier. The images of these

Orthogonal Polynomials 3rd ed

  • Colloquium Publications vol. 23, Amer. Math. Soc., Providence,
  • 1967

Szegö G 1967 Orthogonal Polynomials

  • Szegö G 1967 Orthogonal Polynomials