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The difference between 1st and 2nd quantization is summarized in Figure 08a. In diagram (a) for the 1st quantization, the classical picture of an electron swivelling around the nucleus (as in the hydrogen atom) is replaced by wave function _{} which is a function of r. In this particular case, there are two maxima in the function corresponding to the darker brown and green colors. The averaged circular path is indicated by the circle in blue. The absolute square of the wave function is interpreted as the probability of finding the electron
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## Figure 08a The 1st and 2nd Quantization [view large image] |
at that point. As shown in diagram (a), the interacting medium is the longitudinal component of the electromagnetic field. It is static and by its nature non-relativistic. Such formulation is more suitable for calculating structures in bound state, e.g., in molecules, atoms, ... |

Diagram (b) shows the classical spinor field for a free electron. The 2nd quantization associates the field with a particle. In this example of Compton scattering, which describes the interaction of the electron with a photon, both of them are treated as particles changing states (energy-momentum p, k and/or spin _{p}, polarization ) in the process. The quantum vacuum is now simmering with all kinds of virtual particles popping into existence briefly according to the uncertainty principle t E > (Figure 08a). The celebrated Higgs particle was discovered when it was excited from the virtual Higgs amid the debris in energetic collisions (Figure 08b, also see Higgs Discovery in LHC). As shown in Figure 08a diagram (b), the interaction is now provided by the transverse component of the
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## Figure 08b Higgs Particle from Virtual Higgs |
electromagnetic field A moving with the speed of light and in the form of a particle. Such formalism is relativistic and tailored to the collision of particles for probing into the mechanism within. Both the real and virtual particles |

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