Quantum Mechanics and the Finite Element Method

dx = 0 (1) Here ψ(x) is some sort of wavefunction that somehow describes the properties of the particle, V (x) is the potential the particle moves in, and E is the particle energy. The term ∇ψ(x) ·∇ψ(x) measures the curvature of the wavefunction. In some way it is a surrogate for the (kinetic) energy of the particle. Schrödinger never came to terms with the physical meaning of ψ(x). From this equation, Schrödinger proceeded to carry out an integration by parts. This resulted in an expression involving a second derivative (∇ψ(x)) that we now call Schrödinger’s equation.