Volumetto IV: 24 April 1930 View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2003

AUTHORS

Salvatore Esposito , Ettore Majorana , Alwyn van der Merwe , Erasmo Recami

ABSTRACT

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 $$ M = - e({z_1} + {z_2} + ... + {z_n}) = - ez $$ (4.1) 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 $$ \delta {E_0} = \sum\limits_1^\infty {\frac{{{{\left| {{M_{0k}}} \right|}^2}}}{{{E^0} - {E_k}}}} = \sum\limits_1^\infty {{e^2}} {E^2}\frac{{{{\left| {{z_k}} \right|}^2}}}{{{E^0} - {E_k}}} $$ (4.2) where $$ z\psi 0 = \sum\limits_k {{z_k}} $$ (4.3) More... »

PAGES

319-417

Book

TITLE

Ettore Majorana: Notes on Theoretical Physics

ISBN

978-90-481-6435-6
978-94-017-0107-5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-017-0107-5_4

DOI

http://dx.doi.org/10.1007/978-94-017-0107-5_4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1020638852


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