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Assume that the Planck and DeBroglie relations, E=hand p=h/2, hold for free quantum mechanical particles of mass m. a) Suppose we describe the state of a particle by a plane wave: (x,() = A exp[ikx - iot] Show that the frequency and wavelength (or k and ) are related due to the (non- relativistic) Schroedinger equation for free particles. b) Discuss the dispersive properties of the Schroedinger equation (free case) and find the formula for the phase velocity