The Moments of the Hydrogen Atom by the Method of Brackets

[摘要] 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.

[关键词] non-relativistic hydrogen atom;method of brackets;hypergeometric function;associated Laguerre functions