Density of states

Density of states counts the available states of a system per unit interval of a specified quantity, such as energy or frequency. It connects a system’s allowed states to measurable distributions and response.

State counting: The process of determining how many distinct states satisfy specified conditions. Density of states is obtained by counting states within successive intervals of the measured quantity.
Fermi energy: The energy of the highest occupied electronic state at absolute zero. The density of states near this energy strongly influences a metal’s low-temperature behavior.
Quantum state: A mathematical description of the possible outcomes and properties of a quantum system. Density of states counts distinct quantum states rather than classical trajectories.
Occupation number: The number of particles occupying a specified quantum state. Density of states counts what is available; occupation number describes what is filled.
Phase space: A space whose coordinates specify the possible positions and momenta of a system. In classical systems, counting states often means measuring accessible phase-space volume.
Electronic heat capacity: The contribution of electrons to a material’s heat capacity. Only states near the Fermi energy can be thermally excited, making their density decisive.
Energy eigenstate: A quantum state with a definite energy under a system’s Hamiltonian. Energy-resolved state counts group eigenstates according to their eigenvalues.
Density of states matrix: A matrix-valued description of state density that retains information about internal degrees of freedom. It extends a scalar state count when orbital, spin, or sublattice character matters.
Boundary conditions: Constraints imposed on a system at the limits of its domain. They determine which wave patterns are allowed and therefore alter the state count.
Electrical conductivity: A measure of how readily a material carries electric current. Available electronic states and their distribution help determine which carriers can respond to an electric field.

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