Answer Happy

For the double well system we need to take into account that the particle can tunnel between the left and the right well. We will describe this with a simple model Hamiltonian = Eo - (R) (R] + \L)(LD) - +- (R)(L+ |L)(R) Here Eo describes the energy of the two ground states without the tunnelling and the term t|R) (L| describe that the particle can tunnel from |L) to |R) with some speed described by t and t|L)(R| describe tunnelling in the opposite direction. In the basis {IL), \R)} this Hamiltonian has the matrix representation [10] Îlt = Eo - 11-+-6) [ [ t TO 1] 0 Find the eigenvalues of this matrix and show that the eigenstates are +) = 1. (L) + R))//2.