A molecule is made up of three identical atoms at the corncrs of anequilateral triangle as showi in Fig. 7.12. We consider its ion to be nadeby adding one clectron with some amplitude on cach site. Suppose thematrix element of the Hamiltonian for the electron on two adjacent sites i,j is (i|H|j) =-a for i # j.1o'O?Fig. 7.12(a) Calculate the energy splittings.(b) Suppose an electric field in the z direction is applied, so that tlhepotential energy for the electron on top is lowered by b witli b < Ja|. Nowcalculate the levels.(c) Suppose the electron is in the ground state. Sucdeuly the field isrotated by 120° and points toward site 2. Calculate the probability for theelectron to remain in the ground state.

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