Deriving the path integral formulas from the Schrödinger equation

This paper derives Feynman’s path integral formula from the Schrödinger equation. To this aim, the solution of the Schrödinger equation is expressed by the initial condition and Green’s function. This expression indicates that a wave function at the initial moment propagates to the final state through all possible spatial paths. The iteration of the expression embodies the spirit of the path integral. The Fourier transform of the Green’s function is utilized, which helps to convert the operator Hamiltonian into a numerical one. Then, the latter is spatially discretized, and finally the Hamiltonian is transformed into a Lagrangian. We point out the reason why the Schrödinger equation can be deduced in turn from the path integral formula with a certain approximation.