Ls3_unit_5A - THE INTERACTION OF RADIATION AND MATTER QUANTUM THEORY PAGE VA-1 R Victor Jones APPENDIX THE DIELECTRIC SUSCEPTIBILITY A General

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 5

Ls3_unit_5A - THE INTERACTION OF RADIATION AND MATTER QUANTUM THEORY PAGE VA-1 R Victor Jones APPENDIX THE DIELECTRIC SUSCEPTIBILITY A General

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online