The Exchange operator is a quantum mechanical

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 operator used in the field of quantum chemistry

Quantum chemistry

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...

. Specifically, it is a term found in the Fock operator

Hartree-Fock

In computational physics and chemistry, the Hartree–Fock method is an approximate method for the determination of the ground-state wave function and ground-state energy of a quantum many-body system....

. It is defined as:


where
is the one-electron exchange operator,

are the one-electron wavefunction being acted upon by the Exchange operator as functions of the positions of electron 1 and electron 2,

are the one-electron wavefunction of the j-th electron as functions of the positions of electron 1 and electron 2,

is the distance between electrons 1 and 2.

In Quantum Physics the Exchange Operator can be thought of as a Hermitian operator which swaps the labels on any two identical particles.

See also

• Core Hamiltonian
  Hamiltonian (quantum mechanics)
  In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
  
  

• Coulomb operator
  Coulomb operator
  The Coulomb operator, named after Charles-Augustin de Coulomb, is a quantum mechanical operator used in the field of quantum chemistry. Specifically, it is a term found in the Fock operator...