Article ID: CBB001022003

Schrödinger and Dirac Equations for the Hydrogen Atom, and Laguerre Polynomials (2010)

unapi

It is usually claimed that the Laguerre polynomials were popularized by Schrödinger when creating wave mechanics; however, we show that he did not immediately identify them in studying the hydrogen atom. In the case of relativistic Dirac equations for an electron in a Coulomb field, Dirac gave only approximations, Gordon and Darwin gave exact solutions, and Pidduck first explicitly and elegantly introduced the Laguerre polynomials, an approach neglected by most modern treatises and articles. That Laguerre polynomials were not very popular before their use in quantum mechanics, probably because they had been little used in classical mathematical physics, is confirmed by the fact that, as we show, they had been rediscovered independently several times during the nineteenth century, in published or unpublished studies of Abel, Murphy, Chebyshev, and Laguerre.

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Authors & Contributors
Perovic, Slobodan
Blai Pié i Valls
Burwell, Jennifer
D'Agostino, Salvo
Valente, Giovanni
Stuewer, Roger H.
Concepts
Physics
Quantum mechanics
Mathematical physics
Atomic structure
Mathematics
Philosophy of science
Time Periods
20th century, early
20th century
Places
Italy
Paris (France)
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