Photons waves

Engel V and Metiu H 1994 2-Photon wave-packet interferometry J. Chem. Rhys. 100 5448... 

In (a), two photon waves combine to give a new waveform, which has the same appearance and frequency as the initial separate waves. The photons are said to be coherent, and the amplitude of the waves (light intensity) is simply doubled. In (b), the two photon waves are shown out of step in time (incoherent). Addition of the two waveforms does not lead to a doubling of amplitude, and the new waveform is more complex, composed of a doubled overlapping frequency. In (c), the two waveforms are completely out of step (out of phase) and completely cancel each other, producing darkness rather than light (an interference phenomenon). 

By stipulating that this expression be identical with the quantum relationship 14 w — uj the normalization condition of the photon wave function is obtained... 

It can be shown that when the normalization condition for the photon wave function (50) is satisfied, the vector p can be interpreted as the expectation value of the photon momentum. To do this it is necessary to express p in terms of fk. Substitution of (37) into (51) yields... 

The time-dependence of the photon wave equation in momentum space... 

There are situations in which a definite wave function cannot be ascribed to a photon and hence cannot quantum-mechanically be described completely. One example is a photon that has previously been scattered by an electron. A wave function exists only for the combined electron-photon system whose expansion in terms of the free photon wave functions contains the electron wave functions. The simplest case is where the photon has a definite momentum, i.e. there exists a wave function, but the polarization state cannot be specified definitely, since the coefficients depend on parameters characterizing the other system. Such a photon state is referred to as a state of partial polarization. It can be described in terms of a density matrix... 

The coefficients of this linear combination are not independent since the photon wave function must satisfy the tranversality condition... 

Therefore there are two, not three, different photon states with given quantum numbers j,M. Call these wave functions f M, where A = 0,1. The photon wave function can now be written as a linear combination... 

Photopotential as a fimction of wave length of photons for zinc oxide and cadmium selenide electrodes in aqueous solutions X. = photon wave length. [From Williams, I960.]... 

To be consistent with the physics literature, in this section the incident photon wave function is defined as exp(/k0-r), rather than as exp(— ik0-r). 

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

H is the Hamiltonian which describes the photon wave field ... 

The nonlinear relationship due to the final term causes the wave packet to spread as it propagates. Dropping it assumes that W is so small that the detector can be placed close enough to the scattering target to neglect the spread. Note that only for a photon wave packet is E strictly proportional to k E = tick. The physical situation that we will ultimately consider is that W tends to zero. In section 3.2.2 we showed that the absence of time resolution in an experiment results in the experiment being equivalent to an incoherent superposition of independent experiments, each with an incident plane wave, i.e. an incident wave packet of zero width. 

Equation (6) can be transformed into self-consistent equation for electromagnetic field produced in [1] for the transition in one zone if to fulfill expansion = (dn/ /dk)q, where q = k2 k is the photon wave... 

Once the summation over virtual photon wave-vectors and polarizations in Eq. (5.10) is performed, the result can be cast in terms of a retarded resonance electric dipole-electric dipole interaction tensor V, (a>, R) (Power and Thirunamachandran 1983 Andrews and Sherborne 1987), using the identity... 

The coefficient by the operator (7 in the quantized expansion Eq(54) can be interpreted as the photon wave function ... 

The type , M) of the photon defines the parity. Then the photon wave function in the momentum space with the angular quantum numbers looks... 

The normalization constant C should be chosen in agreement with the normalization of the wave function (77). The photon wave functions in the coordinate space can be obtained with the Fourier transformation of Eq(81). 

The formula (148) presents the final result of the renormalization procedure in QED. It shows that after regularization of the divergent integrals in according to prescriptions (130), (132) and (134) we can replace the initial mass and charge values with the observable ones ttir, cr. After the renormalization is completed for practical calculations we can put Zi = Z3 = 1. This shows that the electron and photon wave functions should remaiin unchanged. 

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