In this article we present the results of our investigations on the ground and the first excited states of a polaron in a polar semiconductor quantum dot in both two and three dimensions. We have also discussed the stability of a strong-coupling bipolaron in quantum dots. We have shown that below a critical value of the confinement length the bipolaron becomes unstable in a quantum dot and breaks up into two individual polarons. We have finally shown that the phonon-induced Zeeman splitting of the first excited level of a two-dimensional parabolic quantum dot becomes strongly size dependent below a certain size and decreases very rapidly with decreasing dot size.

PACS numbers: 68.65.+g, 71.38.+i