On Tamm's problem in the Vavilov-Cherenkov radiation theory

Abstract

We analyse the well-known Tamm problem treating the charge motion on a finite space interval with the velocity exceeding light velocity in medium. By comparing Tamm's formulae with the exact ones we prove that former do not properly describe Cherenkov radiation terms. We also investigate Tamm's formula cos(theta)=1/(beta n) defining the position of maximum of the field strengths Fourier components for the infinite uniform motion of a charge. Numerical analysis of the Fourier components of field strengths shows that they have a pronounced maximum at cos(theta)=1/(beta n) only for the charge motion on the infinitely small interval. As the latter grows, many maxima appear. For the charge motion on an infinite interval there is infinite number of maxima of the same amplitude. The quantum analysis of Tamm's formula leads to the same results.