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2000•American Journal of PhysicsRequires access

Relativistic hydrogen atom revisited

R. P. Martı́nez-y-Romero

Open publisher page 18 citations

Abstract

The hydrogen atom is solved using a simple method. We show that this system has an exact solution that can be written in terms of Laguerre polynomials of noninteger index, instead of the hypergeometric series. This point is important because Laguerre polynomials of integer index appear in the solution of the nonrelativistic hydrogen atom, giving students a more unified point of view for this system.

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What this paper is about

The hydrogen atom is solved using a simple method. We show that this system has an exact solution that can be written in terms of Laguerre polynomials of noninteger index, instead of the hypergeometric series. This point is important because Laguerre polynomials of integer index appear in the solution of the nonrelativistic hydrogen atom, giving students a more unified point of view for this system.

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OpenAlex reports 18 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The hydrogen atom is solved using a simple method. We show that this system has an exact solution that can be written in terms of Laguerre polynomials of noninteger index, instead of the hypergeometric series. This point is important because Laguerre polynomials of integer index appear in the solution of the nonrelativistic hydrogen atom, giving students a more unified point of view for this system.

Key concepts: Laguerre polynomials, Physics, Hydrogen atom, Hypergeometric function, Integer (computer science), Series (stratigraphy), Simple (philosophy), Atom (system on chip)

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