Introducing quantum mechanics through its historical roots: The hydrogen Rydberg atom viewed through the lens of the old quantum theory

M. G. Littman, E. Gordis, P. Zhelnin, J. Arnold

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Solutions of Schrödinger's equation for Rydberg states of hydrogen are shown to display patterns that can be understood semi-classically within the framework of Bohr-Sommerfeld planetary orbits and de Broglie's concept of matter waves. Using n = 10 and n = 100 quantum levels we show how de Broglie-wave-analyzed Kepler orbits can be matched to excited-state wavefunctions and charge distributions. Making the connection between the old and new quantum theories can help beginning students develop an intuition about quantum mechanics and allow them to develop an appreciation of how Schrödinger's wave mechanics was stimulated by the theories of his predecessors.

Original languageEnglish (US)
Pages (from-to)371-378
Number of pages8
JournalAmerican Journal of Physics
Volume91
Issue number5
DOIs
StatePublished - May 1 2023

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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