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BELL SYSTEM TECHNICAL JOURNAL 



natural that the valence electrons should contribute so largely to 

 the binding since the complete shells of electrons making up the Na+ 

 ion, that is the K and L electrons, are only slightly affected by bring- 

 ing the atoms together to form a metal. The result that the energy 

 of the metal is the sum of the energies of the valence electrons is 



ao 



LATTICE CONSTANT IN ANGSTROMS 



Fig. 14 — Energy bands for sodium versus lattice constant. 



of great importance in applying the theory. We shall discuss below 

 how the energies of the various states in the band depend upon the 

 arrangement of the atoms; some of these states are occupied and 

 the energy of the crystal can be found by adding the energies of 

 the occupied states. In this way we can find how the energy of the 

 crystal depends upon the arrangement of the atoms and can find 

 what arrangement makes the energy least. According to theory the 

 arrangement of least energy is the stable one and the one which 

 should be found in nature. The remainder of this section will be 

 devoted to discussing the energies of the quantum states in metals and 

 the energies of the electrons which occupy them. 



The first satisfactory solutions of Schroedinger's equation for elec- 

 trons moving in the field of a metal were obtained for sodium by 

 Wigner and Seitz." They assumed, in keeping with the findings of 

 experirnent, that the sodium atoms were arranged on a body-centered 



11 E. Wigner and F. Seitz, Phys. Rev., 43, 804 (1933) and 46, 509 (1934) and E. 

 Wigner, Phys. Rev., 46, 1002 (1934). 



