Its because the object that nature works with is not the probability distribution but the complex (as in real number plus imaginary number) wavefunction. The pr

Its because the object that nature works with is not the probability distribution but the complex (as in real number plus imaginary number) wavefunction. The probability of being at a location is proportional to the wavefunction squared and the velocity is proportional to the derivative of the wavefunction times the wavefunction (? its been a while). take the function e^(i*x) the magnitude is a constant and so is the magnitude of the derivative.