Solve the below:
Free Particles: Wavefunction, Momentum, and Probability
Q: At t=0, the wavefunction of a free particle is:
psi(x,0) = {(sqrt b/2*pi)sin(bx) for |x|<((2*pi)/b)
{0 for |x|> or = ((2*pi)/b))
a) What is the probability of finding the particle in the interval 0 less than or equal to x less than or equal to pi/2b?
b) What is the momentum amplitude for this wavefunction?
c) For what value of the momentum is the momentum probability maximum?
d) What is the probability for finding the momentum in an interval dp around (h_bar)b?