Theory of Bloch Waves.

Abstract

The Bloch waves of the one-electron theory of electronic states in crystals are the eigenfunctions of a family of unbounded selfadjoint operators H(p) that depend holomorphically on the wave momentum p = (p1, p2, p3) elements of R cubed. H(p) has a discrete spectrum, witth corresponding complete orthonormal sequences of eigenfunctions, and it is customary to denote such a sequence by (psi sub n) (p) and speak of the Bloch waves. However, the eigenfunctions are not unique and a separate choice is required for each p. The customary definitionn therefore rests on the axiom of choice and can provide no information about the p-dependence of the Bloch waves. Some information is essential for applications. A minimal requirements is p-measurability.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA044033

Entities

People

  • Calvin H. Wilcox

Organizations

  • University of Utah

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Analytic Functions
  • Crystal Lattices
  • Eigenvalues
  • Eigenvectors
  • Electronic States
  • Energy Bands
  • Equations
  • Inequalities
  • Integral Equations
  • Integrals
  • Mathematics
  • Momentum
  • Quantum Mechanics
  • Sequences
  • Spectra
  • Theorems

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Linear Algebra
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Microelectronics