1. A particle in a potential well U(x) is initially in a state whose wavefunction (x; 0) is an equal-weight
superposition of the ground state and rst excited state wavefunctions:
(x; 0) = C[ 1(x) + 2(x)] (76)
Show that the value C = 1=
p
2 normalizes (x; 0), assuming that 1 and 2 are themselves normalized.
Determine (x; t) at any later time t.
Show that the average energy hEi for (x; t) is the arithmetic mean of the ground and rst excited state
energies E1 and E2, that is hEi = (E1 + E2)=2.
Determine the uncertainty E of energy for (x; t).
2. Determine the average position hx(t)i of a particle with nonstationary state wave function (x; t) .