Photon energy expectation value

If we now set the frequencies of the exchanged virtual photon to zero, unm —> 0, i.e., if we neglect retardation effects, the energy expectation value reduces to... 

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... 

When 0 < 0 the photon wavepackets that are lined up after each other on the same axis can match their phases and combine into more elongated packets. As a result the linewidth of a single photon is expected to become larger than that of a dense photon beam. The local energy flux density v / should at the same time be given by the number of photons passing a cross-sectional area, regardless of the value of the ratio 0 . 

Figure 5.22 Reduced matrix elements dy, in atomic units, and relative phases (<5y — <5V), in radians, as functions of photon energy for 5p photoionization in xenon leading to the 5p5 2P3/2 final ionic state. The dashed vertical lines give the 2P3/2 and 2P,/2 ionization thresholds at 12.13 and 13.44 eV, respectively. The data in the continuous range above the 2P1/2 threshold are shown as full circles with error bars. The curves below the 2P3/2 and 2P1/2 ionization thresholds are expected to approach the values in the continuum continuously (for details see the discussion and references in the original publication). From [HSS86] the dt given here are larger by /3 in order to adapt them to the cross section...

The very small photodecomposition yields at low temperatures are to be expected in this region, as the photon energy available at 365.0 nm [78.5 kcal/mol is less than that required for dissociation by process 93 and is marginal for process 92 (AH92 = 69.5 kcal/mol, AHg = 89.3 kcal/mol)]. The temperature dependence of these yields has been best explained as a unimolec-ular decomposition of T- with an activation energy of 15 kcal/ mol (176), a value comparable to Ea values found for acetone and hexafluoroace tone. 

All fields and physical constants of the QED Hamiltonian have to be taken as renormalized to avoid divergencies of the electron-electron and electron-photon interaction integrals including the interaction with the external field [41]. Renormalization is independent of die external potential Vg, but requires correction terms, among them an energy correction <5E[Ve ]- Expectation values ( TI I T) of the renormalized QED Hamiltonian are finite for arbitrary N-... 

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