The regular perturbation theory in the strong-coupling polaron problem

Operator method in solving non-linear equations of the Hartree-Fock type

“…The operator method (OM) of the approximate solution of the Schrödinger equation was suggested in the works of Feranchuk and Komarov [1][2][3]. In agreement with the results obtained in these and subsequent works (see, for example, refs.…”

“…Pekar (by Miyake [25]) −0.108 504 Miyake [25] −0.108 513 Adamowski et al [26] −0.108 5128 Feranchuk and Komarov [2] −0.1078 Smondyrev [32] −0.109 206 Efimov and Ganbold [15] −0.108 43 Ganbold and Efimov [16] −0.107 766 Chen et al [27] −0.108 51 Hagen et al [30] −0.020 48 −0.008 04 Balabaev and Lakhno [31] −0.0206 −0.008 32 Our results −0.108 512 8052 −0.020 531 01 −0.008 3506…”

“…The operator method (OM) of the approximate solution of the Schrödinger equation was suggested in the works of Feranchuk and Komarov [1][2][3]. In agreement with the results obtained in these and subsequent works (see, for example, [4][5][6][7][8][9][10][11][12]), the solution in the zeroth approximation of the OM gives quite a simple and universal algorithm for obtaining an approximation, which is uniformly applicable in a wide range of variation of parameters of the Hamiltonian.…”

All-coupling solution for the continuous polaron problem in the Schrödinger representation

“…It leads to the fast convergent series for the solutions of the Schrödinger equation. This method was also applied for regular perturbation series in the polaron problem [25] but it was considered only in the strong coupling limit.…”