a. Suppose that at time ta the state function of a one particle
system is Ψ = (2/πc2)3/4 e(exp [– (x2 + y2 + z2)/c2)] where c = 2
nm. Find the probability that a measurement of the particle’s
position at ta will find the particle in the tiny cubic region with
its center at x = 1.2 nm, y = -1.0 nm, z = 0 and with edges each of
length 0.004 nm. Note that 1 nm = 10-9 m. b. At what point is the
probability density a maximum for the Ψ above. Answer by simply
looking at IΨI2. Compare the result when x is at the origin.