Quantum Theory of the Refractive Index

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Abstract
A slightly refined perturbation theory is used to obtain a unitary transformation which approximately diagonalizes the total Hamiltonian for a system made up of a radiation field in interaction with gas molecules. The dependence of the energy of the total system on the number of photons present gives the usual formula for the refractive index of a gas. The transformation is also applied to the field operators and it is shown that, within the approximations made, the phenomenological Maxwell equations are obeyed in the new representation as equations between certain matrix elements of operators. The transformed representation is also used to derive the Frank-Tamm formula for Čerenkov radiation.