A free particle moving in the r-direction has the normalized wavefunction at t = 0, V (r, t = 0, 0z) = (2102) 1/ exp - 107] (a) Show that V (r, t = 0,0,) is normalized and calculate V (r, t, 0,). (b) Show that the momentum spread Op is Op = 262 and that the position spread is or. Interpret the result in terms of the uncertainty principle. (c) Show that at t > 0 the probability density can be written as |V (r, t ) | = V I,0, Vo Hint: You might use _ _exp [-ar]] de = y a Jaxxexp [-ar'] dx = 203/2, and introduce y = voIty to use _ exp [-ar' - bx] dax = _exp -y* + An dr