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Unformatted text preview: THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE VA-1 R. Victor Jones, April 18, 2000 APPENDIX: THE DIELECTRIC SUSCEPTIBILITY A General Dressed State Formulation Suppose that the complete Hamiltonian of a coupled system is parsed into two components H = H o + H e x . [ VA-1 ] The component H o includes the Hamiltonians for the unperturbed material system, the free radiation field and interactions of the material system with available cavity modes . The component H e x is the Hamiltonian for the interactions which couple the material system to externally excited modes . As the first step in finding a fully quantal expression for the dielectric susceptibility, let us expand the state vector in the Schrödinger picture in terms of, presumably, known eigenkets of H o-- viz. the dressed states of the unperturbed system -- ψ t ( 29 = C s t ( 29 exp- i λ s t ( 29 s s ∑ . [ VA-2 ] Following a now familiar track, we can use the Schrödinger equation of motion -- i.e. i h d dt ψ t ( 29 = H o + H e x [ ] ψ t ( 29 [ VA-3 ] to obtain i h ˙ C r t ( 29 = C q t ( 29 exp- i λ q- λ r ( 29 t [ ] r H e x q q ∑- i h ˙ C r t ( 29 = C q t ( 29 exp + i λ q- λ r ( 29 t [ ] q H e x r q ∑ . [ VA-4 ] In turn, we obtain the following expansion for the time dependent expectation value of induced material system dipole moment: THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE VA-2...
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This note was uploaded on 01/31/2011 for the course PHYSICS 108 taught by Professor Staff during the Winter '08 term at UC Davis.
- Winter '08