For the double well system we need to take into account that the particle can tunnel between the left and the right well

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For The Double Well System We Need To Take Into Account That The Particle Can Tunnel Between The Left And The Right Well 1 (44.51 KiB) Viewed 39 times

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.