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GAUGE INVARIANT FORMULATION
GAUGE INVARIANT FORMULATION WITH SPIN
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A. C. Albrecht absorption band active spectroscopies an(t arrow basis set basis-defining Hamiltonian benzene Bloembergen Chem cm"l cn(t correct Coulomb gauge cross section damping effects dark eigenstates density matrix approach density matrix elements dephasing direct coupling electric field electric-dipole approximation electrical susceptibility electromagnetic potentials electronic emission energy denominator factors equation of motion equivalent evolution exact resonance expansion coefficients expression forward transform Fourier component frequency gauge invariance gauge invariant formulation gauge transformation Hamiltonian HQ(r identity forbidden selection interaction operator intermediate resonances inverse transform material system molecular eigenstates molecule non-Condon non-resonant NONLINEAR OPTICAL obtained one-photon optical spectroscopies perturbation photon Phys physically meaningful position operator principle of gauge probability amplitudes processes pseudo-parity quantum mechanical radiation field Raman scattering REP's resonant secondary radiation s-th SFTPA tensor shown spin forbidden spin-orbit coupling transition amplitudes transition probability amplitudes two-photon absorption vibrational mode vibronic coupling wavefunction