Schrödinger Equation (Strang-Marchuk)

Available identifiers

WikidataQ25303744 ScholiaQ25303744MaRDI QIDQ6674266

second order (Strang-Marchuk) split operator scheme for numerical integration of the time-dependent Schrödinger equation

Defining Formula: $|\psi (t+\Delta t)⟩=\exp (-i\Delta t\hat{T}/(2\hslash ))\exp (-i\Delta t\hat{V}/\hslash )\exp (-i\Delta t\hat{T}/(2\hslash ))|\psi (t)⟩+𝒪(\Delta t{)}^2$

$\Delta t$ symbol represents Time Step

$\hat{T}$ symbol represents Quantum Kinetic Operator

$\hat{V}$ symbol represents Quantum Potential Operator

$\hslash$ symbol represents Planck Constant

$\mathrm{i}$ symbol represents imaginary unit

$\psi (t)$ symbol represents Quantum State Vector (Dynamic)

---