Probability amplitude versus probability distribution

[Morgase]

Homework Statement

The question is "Comment on the physical consequence of two probability distributions being equal to each other even though the probability amplitudes are not the same."

Homework Equations

The Attempt at a Solution

I understand that the modulus squared of the probability amplitude is the probability density which shows the probability of a particle existing at a certain position, but I guess I don't fully understand what the probability amplitude is then. If both particles have the same probability distribution, then they would have the same likelihood of existing in the same position, correct? But what about different prob amps?

 

[Oxvillian]

Knowing the probability distribution is rather like having a photograph of a train. The photograph tells you exactly where the train is, but not which way it's moving. Information about which way the wavefunction is moving is encoded in the amplitude.