Consider a wave function that is a combination of two different infinite well stationary s...

Consider a wave function that is a combination of two different infinite well stationary states, the nth and the mth.

(a) Show that ψ(x,t) is properly normalized.

(b) Show that the expectation value of the energy is the average of the two energies:  (Be careful: The temporal part of the wave function definitely does not drop out.)

(c) Show that the expectation value of the square of the energy is given by

(d) Determine the uncertainty in the energy.