Second-Quantization Formalism

Ingvar Lindgren, John Morrison

Ingvar Lindgren, John Morrison

Emilio Artacho, Lorenzo Miláns del Bosch

A tensorial formalism is presented for the general use of nonorthogonal basis sets in quantum mechanics, both in representation theory and in second quantization. The natural formulation of second quantization for nonorthogonal basis sets defined here is shown to be formally very similar to the usual formulation for orthogonal basis sets. The formalism is used to study orthogonality effects in a Hubbard model defined on a semi-infinite lattice.

Jeppe Olsen

Ning Wu

Second quantization is an essential topic in senior undergraduate and postgraduate level Quantum Mechanics course. However, it seems that there is a lack of transparent and natural derivation of this formalism from the first-quantization one in most existing textbooks. Without introducing the concept of a simple harmonic oscillator and taking the case of an assembly of identical fermions as an example, we provide a less ad hoc derivation of the second quantization formalism based on the equivalence of the fully antisymmetric many-fermion states and the Fock states.