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. 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. Schrödinger's equation, in bra–ket notation, is where H ^ {displaystyle {hat {H}}} is the Hamiltonian operator.