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

Abstract

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