Photon wave function

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... 

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... 

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 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. 

As stated by Milonni [73], An arbitrarily large number n of photons may occupy the same state, and when this situation obtains, it is accurate to regard the photon wave function as defining a classical field distribution. Thus the quantum electrodynamic view of radiation for intense laser fields can be described classically. Overall, the light-matter interaction is treated semi-classically where the diatomic molecule is quantum mechanical and the laser pulse is classical in nature. The electric dipole approximation [74] is also used which reduces the form of the electric field due to the comparative size of the electric field wavelength compared to the molecule. The classical description of the laser field, E r,t), can be written in complex form according to... 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

We shall adopt Eqs. (9-510) and (9-511) as the covariant wave equation for the covariant four-vector amplitude 9ttf(a ) describing a photon. The physically realizable amplitudes correspond to positive frequency solutions of Eq. (9-510), which in addition satisfy the subsidiary condition (9-511). In other words the admissible wave functions satisfy... 

Polarization wave function of photon, 557 Polynomials expansion, 25 Sonine, 25... 

A particle, photon or electron, passing through slit A and striking the detection screen at point x has wave function a( ), while a similar particle passing through slit B has wave function b( )- Since a particle is observed to retain its identity and not divide into smaller units, its wave function ft (x) is postulated to be the sum of the two possibilities... 

As pointed out in Section 7.2, electrons, protons, and neutrons have spin f. Therefore, a system of N electrons, or N protons, or N neutrons possesses an antisymmetric wave function. A symmetric wave function is not allowed. Nuclei of " He and atoms of " He have spin 0, while photons and nuclei have spin 1. Accordingly, these particles possess symmetric wave functions, never antisymmetric wave functions. If a system is composed of several kinds of particles, then its wave function must be separately symmetric or antisymmetric with respect to each type of particle. For example, the wave function for... 

The relationship between different components of orbital angular momentum such as Lz and Lx can be investigated by multiple SG experiments as discussed for electron spin and photon polarization before. The results are in fact no different. This is a consequence of the noncommutativity of the operators Lx and Lz. The two observables cannot be measured simultaneously. While total angular momentum is conserved, the components vary as the applied analyzing field changes. As in the case of spin or polarization, measurement of Lx, for instance, disturbs any previously known value of Lz. The structure of the wave function does not allow Lx to be made definite when Lz has an eigenvalue, and vice versa. 

Space integrals of expressions quadratic in the wave function are interpreted as expectation values of the corresponding physical quantities. This interpretation suggests that (47) should be interpreted as the expectation value of the photon energy, which would mean that... 

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