ABSTRACT
This chapter discusses the perturbative method to obtain the ground and the first excited state energies of quantum-dot polaron in the weak-coupling regime. It also discusses a few standard variational methods to obtain results for the entire range of the coupling constant. The chapter examines the problem of bound polaron in a quantum dot. One of the major issues in the theoretical simulation of a quantum dot is to provide a prescription for the attractive confining potential. Peeters has shown that the positions of the resonance lines in the magneto-optical absorption of a quantum dot with a system of electrons with a parabolic confinement potential is also independent of the electron-electron interaction and the number of electrons in a quantum dot. In addition to quantum dots, other low-dimensional systems that have attracted particular attention are quantum wires, quantum strips, quantum discs, and quasi-one-dimensional systems like carbon nanotubes.
