At time t = 0 a particle is represented by the wave functionwhere A, a, andb are constants...

At time t = 0 a particle is represented by the wave function

where A, a, andb are constants.

(a) Normalize Ψ (that is, find A, in terms of a and b).

(b) Sketch Ψ(x, 0), as a function of x.

(c) Where is the particle most likely to be found, at t = 0?

(d) What is the probability of finding the particle to the left of a? Check your result in the limiting cases b = a and b = 2a.

(e) What is the expectation value of x?