Quantum-mechanical equation for spectroscopic transitions in ordered ferroelectric and ferromagnetic chains

Abstract

Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical ferroelectrically (ferromagnetically) ordered chain of $N$ equivalent elements, interacting with external oscillating electromagnetic field. Landau-Lifshitz equation was represented in Lorentz invariant form by using Hilbert space over the ring of quaternions. It has been shown, that spin vector can be considered to be quaternion vector of the state of the system studied. From comparison with experiment for the first time from pure optical measurements the value of spin $S = 1/2$ for optically active centers - spin-Peierls solitons in carbon chains - has been obtained. The ratio of imagine to real components of complex charge is evaluated for given centers to be $\frac{g}{e} \approx (1.1 - 1.3)10^{2}$.