The Moments of the Hydrogen Atom by the Method of Brackets

TL;DR

This paper introduces a novel application of the method of brackets to compute expectation values of radial powers in hydrogen atom states, providing closed-form solutions as finite sums.

Contribution

It presents a new analytical technique using the method of brackets to evaluate integrals for hydrogen atom expectation values in closed form.

Findings

Closed-form expressions for expectation values derived

Finite sum representations obtained for arbitrary hydrogen states

Method demonstrates effectiveness for quantum radial integrals

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.