Second order approximation for an optical polaron in the strong coupling case

Here we propose a method of construction of the second order approximation for the ground state energy for a class of model Hamiltonians with a linear type of interaction with respect to Bose operators in the strong coupling case. For an application of the above-mentioned method we have considered the polaron model and proposed a set of nonlinear differential equations for the ground state energy calculation in the strong coupling case. We have considered also the radially symmetric case.