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Read or Download Advances in energy transfer processes: proceedings of the 16th course of the International School of Atomic and Molecular Spectroscopy: Erice, Sicily, Italy, 17 June-1 July, 1999 PDF
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Additional info for Advances in energy transfer processes: proceedings of the 16th course of the International School of Atomic and Molecular Spectroscopy: Erice, Sicily, Italy, 17 June-1 July, 1999
Incoherent time evolution of a two-atom system. Characteristic time <* 1/M Transfer rate °c M Incoherent evolution Irreversibility Approach to equilibrium Characteristic time 1/M2 Transfer rate °= M2 Summary In this section we examine the effect of a perturbation represented by an interaction term in the Hamiltonian of a quantum system consisting of two definite states. Two possible pictures emerge: 1 . A coherent time evolution associated with reversibility, oscillations, a characteristic time inversely proportional to the matrix element of the perturbation-Hamiltonian, and a transfer rate proportional to this matrix element.
For many electron atoms the perturbation Hamiltonian is represented by a sum of terms of the type in Eq. 7 with one term for each pair of electrons3. The van der Waals Hamiltonian is responsible for lowering the ground state energy of the two-atom system. The van der Waals bonding is an effect of this interaction. , it leads to energy transfer from one excited atom to the other atom. This is one of several examples of interactions that produce both static and dynamical effects. Summary This section presents a quantum-mechanical treatment of the van der Waals' interaction by considering two hydrogen atoms at such a distance that their wavefunctions do not overlap.
If at time t=T (small), the phase of the wavefunction is interrupted, the change in \c2(t)\2 in time T is A|c 2 (0|Wr 2 (41) and in time t»T \4(ti2^JA\c2(tf^^r=^Tt (42) The probability \c2(t)\2 is now proportional to t and a probability per unit time can be defined _k(flf = ai =' 'T (43) But r =A£ - (44) where AE = width of the transition. Then ^^-T^W^**10 where g(E)=density of final states. If both state / and state 2 are smeared gi(Ei) dEj = probability that state 1 has energy in (Ei, Ei + dEi) (45) 11 g2(E2) dE2 = probability that state 2 has energy in (E2, E2 + dE2) and g(E) in Eq.