Application of hyperspherical coordinates to two-dimensional charged excitons

Hyperspherical coordinates are applied to the bound states of two-dimensional charged excitons. The Schrodinger equation is solved by two different methods, i.e., by a direct expansion in hyperspherical harmonics and by separating it into a radial equation and an angular equation on the basis of the adiabatic approximation. Our main findings are: (a) the low-lying eigenenergies scale nearly linearly with the reduced mass of the exciton; (b) the adiabatic approximation produces a ground-state energy of -1.1384 au, which compares well to -1.1164 au, obtained by hyperspherical expansion in the positronium limit.