Chapter 2 Second Quantisation - TCM Group

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Chapter 2Second QuantisationIn this section we introduce the method of Second Quantisation , the basic framework forthe formulation of many-body quantum systems. The first part of the section focuses onmethodology and notation, while the remainder is devoted to physically-motivated appli-cations. Examples of the operator formalism are taken from various fields of quantumcondensed Notations and DefinitionsSecond Quantisation provides a basic and e cient language in which to formulate many-particle systems. As such, extensive introductions to the concept can be found throughoutthe literature (see, , Feynman s text on Statistical Mechanics [10]). The first partof this section will be concerned with the introduction of the basic elements of secondquantisation, while the remainder of this section will be concerned with developing fluencyin the method by addressing a number of physical us begin by defining the (normalised) wavefunctions| iand corresponding eigen-values of the single-particle Hamiltonian H,viz.

20 CHAPTER 2. SECOND QUANTISATION where n is the total number of particles in state (for fermions, Pauli exclusion en-forces the constraint n =0,1, i.e. n