Can a singe particle have a different wave function for different observers? Suppose someone at rest prepares some electrons with an (close to exact) momentum. In his rest frame the position of the electron is not known. But what kind of wave function will a person see traveling in the same direction and speed of the electron? Would he see that the electron has a (close to exact) position and not know its momentum? Is all that given by one wave function? Or does the wave function change for different observers?