This text outlines a mathematical model for electronic motion at low temperature in a finite, pure sample of a d-dimensional crystal. The authors present research using the machinery of algebraic geometry and topological methods to determine the independent electron approximation. Intended for use by researchers and graduate students in algebraic geometry, analysis and mathematical physics, the book includes chapters on one dimensional algebraic bloch varieties and the potential zero.
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Elsevier Science Publishing Co Inc
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Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-12-282620-7 (9780122826207)
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both from Eidgenossische Technische Hochschule, Zurich, Switzerland
The periodic Schrodinger operator and electrons in a crystal; preliminaries; one dimensional algebraic bloch varieties; compactification and consequences; the potential zero; separable bloch varieties; topology of the family of fermi curves; monodromy; monodromy of separable bloch varieties; monodromy for generic bloch varieties; density of states; density of states and monodromy; the density of states determines the bloch variety.
