  We propose correlated yet extremely simple single-parameter-dependent
wave-functions with a Slater-type correlation factor, to describe excitons in
0D, quasi-1D and quasi-2D semiconductor quantum dots. We provide closed-form
formulas for the wave-function normalization factor, electron/hole
single-particle density and the expectation value of the kinetic energy. We
additionally supply fast integration procedures for the Coulomb interaction in
the presence of dielectric mismatch with the surrounding medium for
nanoplatelets (quasi-2D systems), and for the bare-Coulomb integral in long
nanorods (quasi-1D systems).
