Hi. Does the de Broglie wavelength have any significance for the wavefunctions of particles in a potential that is non-constant in no region of space? As far as I can see, the solutions of the time-independent Schrödinger equation are only sinusoidal if ##E>V=const##. This is enough to derive diffraction and the double-slit-behaviour of electrons and even the energy levels of a particle in a box "the old q.m. way", i.e. without the Schrödinger equation. But is it relevant in a wider context?