Unlike ideal gases where the energy of a gas is a simple sum of the energies of individual particles, in the system of interacting particles the determination of energy levels is very difficult and often impossible task. As a consequence, though the basic ideas and methods for describing the condensed matter can be the same, nevertheless the concrete implementation of these ideas and methods may differ in various cases and types of condensed matter. The occupation number representation (or second quantization) isSecond quantization a convenient formalism for analyzing and describing the quantum many-particle systems with interaction. The description employs the basis of single-particle states as an occupation of each single-particle state with certain number of identical particles.