On the best quadratic approximation in Feynman's path integral treatment of the polaron

The best quadratic approximation to the retarded polaron action due to Adam owski et al. and Saitoh is investigated numerically for a wide range of cou pling constants. The non-linear variational equations are solved iterativel y with an efficient method in order to obtain the ground-stare energy and t he effective mass of the polaron. The virial theorem and expansions for sma ll and large couplings are used to check the high accuracy of the numerical results, Only small improvements over Feynman's (non-optimal) results are observed. For a moving polaron it is shown that the most general quadratic vial action may contain anisotropic terms which, however, do not lead to im provements for the ground-state energy and effective mass. (C) 2001 Elsevie r Science B.V. All rights reserved.