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Spectral properties of reduced Bloch Hamiltonians

✍ Scribed by J.E Avron; A Grossmann; R Rodriguez

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
851 KB
Volume
103
Category
Article
ISSN
0003-4916

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✦ Synopsis

Bloch Hamiltonians are defined, and the existence of bands is proven for a large class of periodic operators. The results are strong enough to include most of the reasonable physical models of a single electron in crystals. A notable exception is the Dirac Bloch Hamiltonian for a Coulombic crystal with high charge. Properties of the Bloch waves are briefly described and it is shown that "simple" Bloch Hamiltonians do not have Bloch waves with a finite number of Fourier coefficients. The asymptotic distribution of the bands is determined, and it is shown that for a large class of Hamiltonians, it is determined by the kinetic energy alone.

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