Quantum Mechanics of Circularly Polarized Photons.
I. General Theory.

抄録

The quantum mechanics of light was worked out first by Dirac. The method of quantum-mechanical description of light has been improved, and many problems on emmissions, absorptions, scatterings, dispersions etc. of light have been treated in succession by many authors. However, the phenomena involving circularly polarized photons have not yet been fully discussed. so far as the present author is aware of.
The most familiar one of such phenomena in an elementary process may be the emission of spectral components in the direction of a magnetic field in the case of the normal Zeeman effect. The polarization of these components has not yet been explained on the basis of the quantum mechanics. Its consequent explanation has been ignored since Lorentz gave it by has electron theory which loses now its general validity.
The purpose of this paper is to work out the quantum mechanics of the circularly polarized light in the form convenient to a practical use. For this purpose the quantum mechanics of a system of photons with definite momenta is summarized in the form independent of their polarizations in the first two sections. The Hamiltonian, the momentum and the spin angular momentum of the system are gin\ven by the equations (2. 4) . The former two have their eigenvalues in this basic states of a second quantization.
We next discuss the transformation of polarization vectors of photons. The transformation from a state of linear polarization to a state in which the spin of the system has also its eigenvalue is determined. We find that such a transformation is unique except a trivial transformation such as (3. 20). It is essentially given by (3. 16) and (3. 17). The energy, the momentum and the spin of the system are transformed into those given by (3. 21).
In the fourth section a system of circularly polarized photons is discussed. We find that the spin has also its eigenvalue in this sysem. We have seen in the previous section that such a polarization state of photons is unique. The basic states of the second quantization in which the spin of the system has its eignvalue are therefore those of an assemblage of circularly polarized photons, and vice versa. In the fifth section the eigenfunction of a system of circularly polarized photons is determined.
In the second part the interaction between phoyons and an atom or a molecule is represented in the form ready to use in the case of any polarization, and the general theory is applied to the polarization of spectral components emitted by an atom in the direction of an applied magnetic field in the case of the normal Zeeman effect. The complete agreement between our theory and the experiment regarding their polarization is verfied.