## Theories of spectral line shape |

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amplitude atom average Baranger Ben-Reuven Boltzmann classical path commutator consider coordinates correlation function corresponding course delta function density matrix diagonal elements diagrams dipole Dirac delta function distribution Doppler Doppler broadening Doppler effect effect eigenvectors electron emitter energy equation evaluate expansion exponential expression factor Fano Feynman diagram Fourier transform frequency given by Eq graphs Greens function Hamiltonian hence imaginary integral intensity interaction interruption approximation Liouville operator Liouvillian Margenau matrix element molecule obviously off-diagonal order to obtain oscillations particle perturber photon Phys poles potential probability propagator quantum radiator reader recall remark replaced resonance broadening result right of Eq Roney Ross Royer satellite scattering second term Section side of Eq spectral line broadening spectral line shape statistical summation suppose term in Eq tion transition treatment upper vector velocity vibrational Voigt profile wave function wherein width yields zero