How is it possible that the wave of an electron (a particle with mass) with a shorter wavelenghth has a faster phase velocity? Does omega (angular frequency) grow faster than k (wave number)? Does it mean that omega is not a linear function of k? 1) If omega and k were always the same then we would have the same phase velocity for every k and omega. 2) If omega is directly proportional to k, it would also mean that their ratio would be the same for every value of omega and k.