The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
Sergei K. Suslov, Benjamin Trey
TL;DR
This paper derives formulas for mean values of powers of r in Coulomb problems using Hahn and Chebyshev polynomials, connecting special functions with quantum mechanics solutions.
Contribution
It introduces closed-form formulas for Coulomb problem mean values expressed through Hahn and Chebyshev polynomials, unifying special functions with quantum solutions.
Findings
Formulas for mean values of r powers in Coulomb problems derived
Connection established between special functions and quantum mechanics
Applicable to both nonrelativistic and relativistic cases
Abstract
We derive closed formulas for mean values of all powers of r in nonrelativistic and relativistic Coulomb problems in terms of the Hahn and Chebyshev polynomials of a discrete variable. A short review on special functions and solution of the Coulomb problems in quantum mechanics is given.
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