Book contents
- Frontmatter
- Contents
- Preface
- I Classical mathematics and physics
- II Bound states in quantum mechanics
- 4 Time-independent quantum mechanics
- 5 Independent-electron models
- 6 Time-dependent theory and linear response
- III Continuum states and scattering theory
- IV Field theories
- References and bibliography
- Index
5 - Independent-electron models
Published online by Cambridge University Press: 23 December 2009
- Frontmatter
- Contents
- Preface
- I Classical mathematics and physics
- II Bound states in quantum mechanics
- 4 Time-independent quantum mechanics
- 5 Independent-electron models
- 6 Time-dependent theory and linear response
- III Continuum states and scattering theory
- IV Field theories
- References and bibliography
- Index
Summary
Despite the simple and universal structure of the nonrelativistic Hamiltonian for N interacting electrons, it produces a broad spectrum of physical and chemical phenomena that are difficult to conceptualize within the full N-electron theory. Starting with the work of Hartree [162] in the early years of quantum mechanics, it was found to be very rewarding to develop a model of electrons that interact only indirectly with each other, through a self-consistent mean field. A deeper motivation lies in the fact that the relativistic quantum field theory of electrons is explicitly described by a field operator that corresponds more closely to a oneparticle model wave function than to that of the Schrödinger N-electron theory. The fundamental characterization of this electron field by Fermi–Dirac statistics is directly applicable to the mean-field theory, using concepts of statistical occupation numbers determined by effective one-electron orbital energy values. The variational theory appropriate to such independent-electron models is developed in this chapter.
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- Publisher: Cambridge University PressPrint publication year: 2002