Second Quantization of Matter

Abstract

In this chapter we discuss the second quantization of the non-relativistic matter field, that is the Schrödinger field. We show that the Schrödinger field can be expressed as a infinite sum of harmonic oscillators. These oscillators, which describe the possible eigenfrequencies of the matter field, are quantized by introducing creation and annihilation operators acting on the Fock space of number representation.

Further Reading

For the second quantization of particles and non-relativistic quantum field theory:

N. Nagaosa, Quantum Field Theory in Condensed Matter Physics, Chap. 1, Sects. 1.1 and 1.2 (Springer, Berlin, 1999)

A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems, Chap. 1, Sects. 1.1 and 1.2 (Dover Publications, New York, 2003)

H.T.C. Stoof, K.B. Gubbels, D.B.M. Dickerscheid, Ultracold Quantum Fields, Chap. 6, Sects. 6.1, 6.2, 6.3, and 6.4 (Springer, Berlin, 2009)

A. Atland, B. Simons, Condensed Matter Field Theory, Chap. 2, Sect. 2.1 (Cambridge University Press, Cambridge, 2006)

For the quantum properties of bosons in a double-well potential:

G. Mazzarella, L. Salasnich, A. Parola, F. Toigo, Coherence and entanglement in the ground-state of a bosonic Josephson junction:from macroscopic Schrdinger cats to separable Fock states. Phys. Rev. A 83, 053607 (2011)