A particle is described by the wave function ψ(x) = b(a^2 - x^2) for -a ≤ x ≤ +a and ψ(x) = 0 for x ≤ -a and x ≥ +a, where a and b are positive real constants.
(a) Using the normalization condition, find b in terms of a.
(b) What is the probability to find the particle at x = +a/2 in a small interval of width 0.010a?
(c) What is the probability for the particle to be found between x = +a/2 and x = +a?