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9: Many-Body Problems in Quantum Mechanics

Last updated

Nov 26, 2021
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- 8.4: Bose-Einstein and Fermi-Dirac Statistics
- 9.1: Interacting Electrons in Atomic Shells

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In this final section we study a variety of problems in many-body quantum mechanics. First, we introduce the Hartree-Fock method for taking into account the effect of electron-electron interactions in atoms. Next, we describe spin waves in magnetic materials using the Heisenberg model. Third, we describe the behaviour of an atom interacting with photons in a cavity, and introduce the Jaynes-Cummings Hamiltonian. And finally, we take a brief look at the basic ideas behind quantum field theory.

9.1: Interacting Electrons in Atomic Shells
9.2 Spin Waves in Solids
9.3: An Atom in a Cavity
9.4: Outlook: Quantum Field Theory
We have surreptitiously introduced the basic elements of non-relativistic quantum field theory. Consider again the Heisenberg model, where we described a lattice of spins with nearestneighbour interactions. If we take the limit of the lattice constant a→0 we end up with a continuum of creation and annihilation operators for each point in space. This is a field.

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