Volumetto IV: 24 April 1930

  • Salvatore Esposito
  • Ettore MajoranaJr
  • Alwyn van der Merwe
  • Erasmo Recami
Part of the Fundamental Theories of Physics book series (FTPH, volume 133)


Let us consider an atom with n electrons in the ground state, which we will assume is an s level described by the eigenfunction ψ 0 corresponding to the eigenvalue E 0. The component of the electric moment along the z axis is given by
$$ M = - e({z_1} + {z_2} + ... + {z_n}) = - ez $$
with z = z 1 +z 2+...+z n . An electric field of intensity E acting along the z axis induces a perturbation of the atom that depends on the potential EM = H. Assuming that the ground state is not degenerate or, more precisely, that no p levels correspond to the eigenvalue E 0, the element M 00 of the perturbation matrix certainly vanishes. Consequently, for weak fields the variation of the eigenvalue is given by the second-order formula
$$ \delta {E_0} = \sum\limits_1^\infty {\frac{{{{\left| {{M_{0k}}} \right|}^2}}}{{{E^0} - {E_k}}}} = \sum\limits_1^\infty {{e^2}} {E^2}\frac{{{{\left| {{z_k}} \right|}^2}}}{{{E^0} - {E_k}}} $$
$$ z\psi 0 = \sum\limits_k {{z_k}} $$


Theoretical Physic Plane Wave Discrete State Spherical Function Hankel Function 
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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Salvatore Esposito
    • 1
  • Ettore MajoranaJr
    • 2
  • Alwyn van der Merwe
    • 3
  • Erasmo Recami
    • 4
  1. 1.University of Naples “Federico II”NaplesItaly
  2. 2.Italian National Institute for Nuclear PhysicsSite of PisaItaly
  3. 3.University of DenverDenverUSA
  4. 4.University of BergamoDalmine (BG)Italy

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