ls3_unit_5A

ls3_unit_5A - THE INTERACTION OF RADIATION AND MATTER...

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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 ex . [ 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 ex 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 ( ) = C s t ( ) exp i λ s t ( ) 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 ( ) = H o + H ex [ ] ψ t ( ) [ VA-3 ] to obtain i h ˙ C r t ( ) = C q t ( ) exp i λ q − λ r ( ) t [ ] r H ex q q i h ˙ C r t ( ) = C q t ( ) exp + i λ q − λ r ( ) t [ ] q H ex r q . [ VA-4 ] In turn, we obtain the following expansion for the time dependent expectation value of induced material system dipole moment:
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THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE VA-2 R. Victor Jones, April 18, 2000
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ls3_unit_5A - THE INTERACTION OF RADIATION AND MATTER...

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