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

where A, a, andb are constants.

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

(b)?Sketch ?(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?

V(x,0) = A, A 0, (b-x) (b-a) if 0 x a, if a x b, otherwise,