Beyond the Schrödinger Equation

In this chapter we exploit the possibilities of stochastic electrodynamics to carry the theory beyond the usual limits of Schrodinger’s quantum mechanics and enter the province of (nonrelativistic) quantum electrodynamics. The equation of evolution for the mean energy, derived in Chap. 4, is employed to obtain the formulas for the radiative lifetimesLifetime and make contact with the Einstein A and B coefficients.Zeropoint!and A-B coefficients A-B coefficients Further, small correctionsQuantum corrections to the energy of the atomic levels are shown to be due to the fluctuationsFluctuations of the dynamical variables. Without the need to use perturbation theory—because the zero-point fieldFluctuations!zero-point field is there from the beginning—the correct formulas are obtained for the Lamb shiftLamb shift Cavity effects!on the Lamb shiftand other radiative effects, to lowest order. The second part of the chapter is devoted to an inquiry about the origin of the spinSpin of the electronPolarization!and spin. Just as it gives rise to position, momentumMomentum and energyZeropoint!energy fluctuationsZeropoint!energy fluctuations Spin!and fluctuations Fluctuations!momentum, the zero-point field is seen to induce an angular momentum resulting from the instantaneous torque exerted by the Lorentz forceLorentz!force on the particle. A close analysis based on the separation of the field modes of given circular polarization Polarization!circularreveals the existence of a spin angular momentum of value \(\hbar /2\), and of a corresponding magnetic momentMoment!magnetic Magnetic moment with a \(g\)-factor of value 2. This allows us to identify the spin of the electron as a further emergent property, generated by the interaction of the particle with the zero-point field.