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Everything You Always Wanted to Know About the Hydrogen Atom (But Were Afraid to Ask)

Randal C. Telfer
Johns Hopkins University

May 6, 1996


A thorough review of the structure of the hydrogen atom will be presented with emphasis on the quantum-mechanical principles involved rather than calculational detail, which will be minimized. First, the relationship of the Heisenberg uncertainty principle to the hydrogen atom will be discussed briefly. This is followed by a discussion of the energy level structure of the hydrogen atom, including fine structure, in the context of the quantum-mechanical theories of Bohr, Schrödinger, and Dirac. Finally, smaller-order corrections to these theories will be discussed, including the Lamb shift, hyperfine structure, and the Zeeman effect.

To the reader:

I wrote this article in connection with a talk given on March 4, 1996 for the second-year graduate seminar class in the Henry A. Rowland Department of Physics and Astronomy at the Johns Hopkins University. My intention is to provide the physics student with a solid review of the physical principles, particularly from quantum mechanics, that pertain to the structure of the hydrogen atom. In the interest of making the article of moderate length, some basic material is excluded, so it is assumed that the reader has at least some familiarity with basic quantum mechanics. The article should thus be at a good readable level for the graduate or upper-level undergraduate physics student. My specific goal in writing this paper was to provide a review appropriate for physics graduate students at Johns Hopkins to prepare for oral exams.

I would greatly appreciate comments on this article, particularly how it could be improved. Please send mail to

I would like to thank Dr. Richard Henry and Dr. Chung Kim for reminding me of the importance of this material.

I would also like to thank Guoan Hu for his help in converting this document to html.

Download this paper as a gzipped postscript file (340 kb)

Randal Telfer
Fri Jun 14 19:03:53 EDT 1996