AN EXTENSIVE CALCULATION OF THE PROPERTIES OF A ONE-DIMENSIONAL POLARON

A refined approach where the wave function is gradually improved is de veloped in the one-dimensional (1D) large-Frohlich-polaron problem. Th e results for the ground-state energy, the effective mass, and the ave rage number of virtual phonons are obtained for a wide range of the co upling constant alpha, and are in agreement with those of the Feynman path-integral formalism. In addition, in the weak-coupling limit, the expansions of these observables in powers of the coupling constant are exactly calculated up to the alpha3-term. They are E = -alpha - 0.060 66alpha2 - 0.008 44alpha3, m = 1 + 0.5alpha + 0.5alpha + 0.191 94alp ha2 + 0.069 12alpha3, and N = 0.5alpha + 0.121 32alpha2 + 0.029 54alph a3, which agree with the known results of the fourth-order perturbatio n theory.