Phonon and Electron Coupling

We have seen that it is possible to derive frictional forces arising from coupling of the molecule motion to inelastic excitations in the solid. Thus with the models developed in Chapter 8 and in this chapter we find that the motion of the 

FiQURE 11.5 The upper panel shows the intermolecular bond distance r t) and the distances Zi(t) (/ = 1,2) from the surface for the two deuterium atoms in D2 colliding with a copper surface at 300 K. The initial kinetic energy is 77.5 kJ/mol and initial vibratlonal/rotational state V = j = 0. The lower panel shows the static potential Vq, the potential Vadd arising from the phonon coupling, and the energy transfer to the solid Eint as a function of time (in units of 10 fs). 

2 Show eq. (11.38). Hint Use the fact that the number of states on the energy shell is d/dE)N E), where N E) is the number of states with energy less than E. Also use the relation /six axdx — (l/2)x — /4a)s n2ax. 

3 Show that the phase factor in eq. (11.17) makes the wavefunction antisymmetric in integralchange of two particles. 

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