Liouville-von Neumann Equation
type: Item
instance of: mathematical expression
instance of: continuous-time expression
in defining formula: H ^
in defining formula: ρ ^
in defining formula: ℏ
in defining formula: t
in defining formula: i
community: MathModDB
MaRDI profile type: MaRDI formula profile
defining formula: ∂ ρ ^ ∂ t = − i ℏ [ H ^ , ρ ^ ]
contains: Quantum Hamiltonian (Electric Charge)
contains: Quantum Hamiltonian (Electric Polarizability)
contains: Quantum Hamiltonian (Electric Dipole)
specialized by: Schrödinger Equation (Time Dependent)
specialized by: Classical Liouville Equation
Wikidata QID: Q2533076
description: Just as the Schrödinger equation describes how pure states evolve in time, the Liouville-von Neumann equation describes how a density operator evolves in time. Note that there can be different density operators for pure or for mixed states.
description: Note the similarity with the classical Liouville equation where the commutator brackets [.,.] are replaced by Poisson brackets {.,.}
related URL: Von Neumann equation for time evolution
named after: John von Neumann
named after: Joseph Liouville
description: describes how a density operator (for pure or for mixed states) evolves in time
alternative label: Quantum Liouville Equation
alternative label: von Neumann equation