PPT Slide
De Broglie and experiment have told us the wavelength of a particle with momentum p, ?=h/p but what if the particle is rolling up a hill: it will eventually turn around and roll down again. Suppose the hill has a very gentle slope, so that the momentum is not changing much in a distance h/p, then the de Broglie formula must give the wavelength pretty accurately. As the particle rolls up the hill, p goes down and the wavelength goes up. We see that the wavelength depends on the local potential energy--- we are going to need a wave equation that contains the potential energy U(x)