Two-dimensional quantization rule for the bound-state spectra in quantum dots

We study the bound-state spectra for three physically important problems in quantum dots, which are in central force potentials and confined in a two-dimensional disc of radius r0, by the quantization rules obtained by the analytical transfer matrix method (ATMM). Comparison of the energy eigenvalues by ATMM with those by WKB reveals WKB cannot hold true when r0 is small, whereas ATMM is better accuracy.