(III) Now suppose that the wave function for an electron at time t 0 is given by (r, 0) = A sin (Tx/L) where A is a suitable normalization constant. Which one of the following is the wave function at time t? (a) (r, t) = A sin (Tx/L) cos (Est/h) (b) (r, t) = A sin (Tx/L)e-iEst/h (c) Both (a) and (b) above are appropriate ways to write the wave function. (d) None of the above. (IV) The wave function for an electron at time t = 0 is given by (x, 0) = A sin (rx/L) where A is a suitable normalization constant. Which one of the following is true about the probability density (r, t) after time t? (a) (x, t)P = |AP sin" (rx /L) cos?(Est/h). (b) (r, t)P AP sin1"(7/L)e-i2Est/h. (c) (a, t)P = |A|P sin" (rx/L) which is time-independent. (d) None of the above. 5