Schrödinger Equation (Second Order Differencing)

Available identifiers

MaRDI QIDQ6674270

second order differencing scheme for numerical integration of the time-dependent Schrödinger equation

Description

Essentially a symmetric (and symplectic!) combination of Euler forward and backward methods.

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Defining Formula: $|\psi (t+\Delta t)⟩=|\psi (t-\Delta t)⟩-2i\Delta t\hat{H}/\hslash |\psi (t)⟩+𝒪(\Delta t{)}^3$

$H$ symbol represents Quantum Hamiltonian Operator

$\Delta t$ symbol represents Time Step

$\hslash$ symbol represents Planck Constant

$\mathrm{i}$ symbol represents imaginary unit

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

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