Green's function works by solving the Schrödinger equation, which describes the quantum state of a system. It essentially provides the response of the system to a delta function source. In mathematical terms, if L is a linear differential operator and δ(x) is the Dirac delta function, then Green's function G(x, x') satisfies:
L G(x, x') = δ(x - x')
Once Green's function is known, the solution to the inhomogeneous differential equation Lψ = f can be expressed as:
