Quantum Mechanics of One- and Two-Electron Systems

  • H. A. Bethe
  • E. E. Salpeter
Part of the Encyclopedia of Physics / Handbuch der Physik book series (HDBPHYS, volume 7 / 35)


One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons. For hydrogen and the analcgous ions He+, Li++, etc., the calculations can be performed exactly, both in Schrödinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron. More specifically, the calculations are exact for a single electron in a fixed Coulomb potential. Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics. For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy. Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible. Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment.


Principal Quantum Number Lamb Shift Bear Approximation Magnetic Quantum Number DIRAC Theory 
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© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1957

Authors and Affiliations

  • H. A. Bethe
  • E. E. Salpeter

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