Relation between Schrödinger's equation and the path integral formulation of quantum mechanics
This article relates the Schrödinger equation with the path integral formulation of quantum mechanics using a simple nonrelativistic one-dimensional single-particle Hamiltonian composed of kinetic and potential energy. == Background == === Schrödinger's equation === Schrödinger's equation, in bra–ket notation, is i ℏ d d t | ψ ⟩ = H ^ | ψ ⟩ {\displaystyle i\hbar {\frac {d}{dt}}\left|\psi \right\rangle ={\hat {H}}\left|\psi \right\rangle } where H ^ {\displaystyle {\hat {H}}} is the Hamiltonian operator.