Ground state energy of polaron bound in a Coulomb potential

The path integral method is used to obtain an expression, involving a sum over the complete set of solutions for the effective trial Hamiltonian, for the ground state energy of the bound polaron. The numerical calculations of this expression are performed for the hydrogenic and harmonic oscillator effective potentials. The present method together with several previous theories and their numerical results are discussed over a wide range of the electron–phonon coupling constant α and the electron–massive hole coupling β. It is shown that, for the experimentally important region, the present method with the hydrogenic potential yields the lowest energy—slightly lower than obtained by the Larsen's variational calculation.