The Moments of the Hydrogen Atom by the Method of Brackets

Abstract

Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in closed-form and to produce an expression for this average value as a finite sum.

References in corpus (7)

• Optimized Negative Dimensional Integration Method (NDIM) and multiloop Feynman diagram calculation
• Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems
• The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
• Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams
• Definite integrals by the method of brackets. Part 1
• Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams II
• Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II

Cited by in corpus (3)

• New sum rules for Wigner 3jm symbols: application to expectation values of hydrogenic ions
• Quadratic and quartic integrals using the method of brackets
• Evaluation of the second virial coefficient for the Mie potential using the method of brackets