General Laws of Optical Transitions

  • Hermann Haken
  • Hans Christoph Wolf
Part of the Advanced Texts in Physics book series (ADTP)


Selection rules and symmetry considerations play a basic role in modern physics. This holds for the atomic shells, the nucleus, elementary particles and for many other areas. We shall present only a small but typical sample here, taking up the perturbation theory discussed in Sect. 15.2. We began with the unperturbed wavefunctions φ n . The perturbation Hamiltonian in one example contained the dipole moment ez. In the following, we shall first choose the x coordinate instead of the z coordinate. We became acquainted with matrix elements of the form
$$ H_{mn}^P = \smallint \phi _m^*(r)ex{\phi _n}(r)dV$$
as important parameters. As we observed at that time, there are a number of realistic cases in which matrix elements vanish when the indices m and n are equal, on the basis of symmetry alone. We shall now examine these cases.


Matrix Element Dipole Moment Selection Rule Radiation Field SchrOdinger Equation 
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  1. E.U. Condon, G.H. Shortley: The Theory of Atomic Spectra ( Cambridge University Press, Cambridge 1991 )Google Scholar
  2. I.I. Sobelman: Atomic Spectra and Radiative Transitions, Springer Ser. on Atoms and Plasmas, Vol. 12, 2nd corr. ed. ( Springer, Berlin Heidelberg 1997 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hermann Haken
    • 1
  • Hans Christoph Wolf
    • 2
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgartGermany
  2. 2.Physikalisches InstitutUniversität StuttgartStuttgartGermany

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