Suppose we have a coupled potential well consisting of two weakly coupled identical potential wells with a barrier between them. We presume that we have solved this problem approximately using a tight-binding approach for the lowest two coupled states, giving approximate solutions

1 W - ( 2 ) J2 (Wleft ( z ) + Wright (=)) and us+ (2) = (Wleft ( z ) - Wright (=) ) with associated energies E = E1 +AE where E, is the energy of the lowest solution in either of the potential wells considered separately, Wleft (z) is the corresponding wavefunction of the first state in the left well considered separately, Wright ( z) is the corresponding wavefunction of the first state in theright well considered separately, and AB is a number that has been calculated based on the coupling. Suppose now that the coupled system is initially prepared, at time I = U , in the state such that the particle is in the left well, with initial wavemction Wie (z). (i) Calculate expressions for the wavemction and the probability density as a function of time after t: 0. (ii) Describe in words the time-dependence of this probability density