Contrast this to classical mechanics where the time development of the momentum is given by and the time development of position is given by . Or in the Lagrangian formulation the time development of the generalized coordinates is given by the second order differential equations known as the Euler-Lagrange equations. Let's move on to the next postulate. Postulate 3 is where we find out what the wave function really means . The basic postulate in quantum mechanics is that the wave function is related to the probability for finding a particle at position x .
P is the probability for finding the particle somewhere between A and - A .
All of the above discussion is part of Postulate 3. The probabilistic interpretation of the wave function is what sets quantum mechanics apart from all other classical theories. It is totally unlike anything you will have studied in your other physics courses. The acceleration or position of a particle, represented by the symbols and x , are well defined quantities in classical mechanics. However with the interpretation of the wave function as a probability density we shall see that the concept of the definite position of a particle no longer applies.