Schrödinger Equation (Time Dependent)
type: Item
instance of: mathematical expression
instance of: continuous-space expression
instance of: continuous-time expression
description: One of the fundamental postulates of Quantum Mechanics on the time evolution of quantum states.
defining formula: i ℏ ∂ ∂ t | ψ ( t ) ⟩ = H ^ | ψ ( t ) ⟩
in defining formula: H
in defining formula: ℏ
in defining formula: ψ ( t )
in defining formula: t
in defining formula: i
community: MathModDB
MaRDI profile type: MaRDI formula profile
contains: Quantum Hamiltonian (Electric Charge)
contains: Quantum Hamiltonian (Electric Polarizability)
contains: Quantum Hamiltonian (Electric Dipole)
contains: Planck Constant
contains: Quantum Hamiltonian Operator
contains: Quantum State Vector (Dynamic)
contains: Time
specialized by: Classical Hamilton Equations
specialized by: Schrödinger Equation (Time Independent)
specialized by: Classical Newton Equation
specialized by: Darwin-Howie-Whelan Equation for a Strained Crystal
specialized by: Darwin-Howie-Whelan Equation for an Unstrained Crystal
specialized by: Heavy Particle Newton Equation
specialized by: Light Particle TDSE
specialized by: Light Particle TISE
Wikidata QID: Q165498
discretized by: Schrödinger Equation (Strang-Marchuk)
discretized by: Schrödinger Equation (Second Order Differencing)
discretized by: Schrödinger Equation (Chebychev Polynomial)
discretized by: Schrödinger Equation (Differencing Scheme)
discretized by: Schrödinger Equation (Lie-Trotter)
discretized by: Schrödinger Equation (Split Operator)
assumes: Closed System Approximation
named after: Erwin Schrödinger
description: partial differential equation describing how the quantum state of a non-relativistic physical system changes with time