Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.

Ok so a particle moves in the x-direction(with V(x) = 0). The state of system is represented by    which is a superposition of energy - momentum eigenfunctions and f(k) represents ,   a) what is the group velocity associated with this state. b)What is the probability for measuring particle at position x=x0>0 at time t=t0>0? And also what is probability per unit length?
What is the physical meaning of the desired results? If anyone could give me some insight that would be greatly appreciated thank you.