In the limit of strong electron-phonon coupling, we use either a Pekar-type or an oscillator wave function for the center-of-mass coordinate and either a Coulomb or an oscillator wave function for the relative coordinate, and are able to reproduce all the results from the literature for the large-bipolaron binding energy. Lower bounds are constructed for the critical ratio g, of dielectric constants below which bipolarons can exist. It is found that, in the strong-coupling limit, the stability region for bipolaron formation is much larger in two dimensions (2D) than in 3D. We introduce a model that combines the averaging of the relative coordinate over the asymptotically best wave function with a path-integral treatment of the center-of-mass motion. The stability region for bipolaron formation is increased compared with the full path-integral treatment at large values of the coupling constant a. The critical values are a, =9.3 in 3D and a, =4.5 in 2D. Phase diagrams for the presented models are also obtained in both 2D and 3D.

We consider a model describing the one-dimensional confinement of an exciton in a symmetrical, rectangular quantum-well structure and derive upper and lower bounds for the binding energy E b of the exciton. Based on these bounds, we study the dependence of E b on the width of the confining potential with a higher accuracy than previous reports. For an infinitely deep potential the binding energy varies as expected from 1 Ry at large widths to 4 Ry at small widths. For a finite potential, but without consideration of a mass mismatch or a dielectric mismatch, we substantiate earlier results that the binding energy approaches the value 1 Ry for both small and large widths, having a characteristic peak for some intermediate size of the slab. Taking the mismatch into account, this result will in general no longer be true. For the specific case of a Ga 1−x Al x As/GaAs/Ga 1−x Al x As quantum-well structure, however, and in contrast to previous findings, the peak structure is shown to survive.

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We discuss the (LO)polaron dispersion for arbitrary spatial dimension D. Firstly, we review the existing literature; recent numerical work is critically analyzed. Secondly, we derive novel upper bounds for the dispersion, which incorporate the correct behaviour of the dispersion up to third order of the coupling constant a. A totally analytical evaluation is performed in the case D ¼ 1. We compare the upper bounds with previously published lower bounds. Apart from a surrounding of zero dispersion, the relative deviation is on a few-percent scale.