# How is it possible that the wave of an electron (a particle with mass) with shorter wavelenghth has a faster phase velocity?

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.

• What do you think is the relationship between omega and k for a free particle?
– nasu
Apr 15 at 14:26
• Let´s say that it´s k squared divided by 2m. Apr 15 at 17:52
• Then what is your question? Is this a linear relationship?
– nasu
Apr 15 at 19:04
• No, it´s not. So, the bigger is the wave number (shorter wavelength), the bigger is the ratio between the angular frequency and the wave number (phase velocity). Apr 15 at 20:30