One-dimensional polarons and bipolarons in the strong coupling limit

In this thesis the one-dimensional (1D) polaron and bipolaron are studied in the strong-coupling limit. In this limit the adiabatic approximation leads to exact equations.; The 1D polaron problem is solved in different external potentials. Besides the study of the ground state also the excited states of the 1D polaron are considered. We study also how the limit to infinity is reached starting from a box with a finite length. It is found that the energies then combine into two groups. This limit also demonstrates the existence of a whole set of energy levels which do not appear while solving the problem on an infinite axis. By scaling to 2D and 3D we obtain also information about the energy spectrum corresponding to the radial excitations of the 2D or 3D polaron respectively.; The nonlinear effective Schrodinger equation is also solved on a thin ring. We obtain the energies and real wave functions of the ground state and excited states. Also the complex wave functions are studied which correspond to energy levels with finite angular momentum.; The equations for the wave function, ground state energy and effective mass of the 1D bipolaron in the strong-coupling limit are derived. We arrive at two equations: the variational equation and the Schrodinger equation. Both of them can be used to solve the bipolaron problem.; Based on these equations the numerical study of the 1D bipolaron is performed. The main characteristics (e.g. the energy, the stability region, etc.) of one 1D bipolaron are considered. An enlargement of the stability region for the 1D bipolaron ground state is found as compared to the stability regions scaled from 2D or 3D. In the limit of an infinitely large box and in the strong-coupling limit the ground state is bound and the first RES has an energy which equals the energy of two single polarons. Because of symmetry reasons some grouping of the energy levels corresponding to the excited states appears. To explain this grouping we show how the 1D bipolaron call be constructed starting from the 1D polaron wave functions. This investigation also leads to the conclusion that the nonlinearity of the equations causes the feature that the combination of the ground state and an excited state of one-particle wave functions could lead to a higher energy than the combination of two excited states.