Permanent (mathematics) in the context of Hartree–Fock method

In computational physics and chemistry, the Hartree–Fock (HF) method is used for approximating the wave function and the energy of a quantum many-body system in a stationary state. It is named after Douglas Hartree and Vladimir Fock.

The Hartree–Fock method often assumes that the exact ${\displaystyle N}$-body wave function of the system can be approximated by a single Slater determinant (in the case where the particles are fermions) or by a single permanent (in the case of bosons) of ${\displaystyle N}$ spin-orbitals. By invoking the variational method, one can derive a set of ${\displaystyle N}$ coupled equations for the ${\displaystyle N}$ spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining exactly solvable Hamiltonians.