Just starting QM & am looking at TISE & how it builds from start & need a little help understanding. OK, for a free particle the de Broglie wave function is ψdB(x,t) = Aei(kx-ωt) where A is a complex constant this corresponds t a free particle with momentum magnitude p = h/λ = hbar k & energy E = hf = hbar ω good so far . . . . . my text book then asks what partial differential equation this wave fuction satisfies & suggests a suitable pde; i hbar dψdB/dt = - hbar2/2m d2ψdB/dx2 Really not sure why this partial differential equation. What goes on? Help if possible, please.