For a two-level system, the optical Bloch equations describe the time evolution of this quantity, which is proportional to its commutator with the Hamiltonian according to von Neumann's theorem.
One set of equations for this quantity can be cast in a simple and real form by substituting pseudospin for this quantity. In a non-degenerate ergodic system, this quantity depends only on the energy and has components proportional to the Kronecker delta, while at thermal equilibrium, this quantity is a constant of the motion and thus must commute with the Hamiltonian. For a two-level system, the optical Bloch equations describe the time evolution of this quantity, which is proportional to its commutator with the Hamiltonian according to von Neumann's theorem. Expectation values of observables can be computed by multiplying the associated operator by this quantity and taking the trace of the result. The coefficients of the orthonormal expansion of the wavefunction in terms of basis states are the components of, for 10 points, what quantity which contains a complete description of a quantum mechanical system?
One set of equations for this quantity can be cast in a simple and real form by substituting pseudospin for this quantity.
density matrix [or density operator]