The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.

International Journal of Modern Physics BAug 15, 199411 citations

RELATIVISTIC RADIATION TRANSITIONS

F. A. Babushkin

Optics and SpectroscopyJul 1, 19654 citations

Wave Mechanics of Radiation and Free Particles

Earle H. Kennard

The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed $\frac{h}{\mathrm{mc}}$ ( $m=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{particle}$ ). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed $\frac{h}{\mathrm{mc}}$ ($m=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{particle}$). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.

Physical ReviewFeb 1, 19322 citations

\frac{h}{\mathrm{mc}}

(

m=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{particle}

). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.