  The properties of energy spectrum of excitons in monolayer transition metal
dichalcogenides are investigated using a multiband model. In the multiband
model we use the excitonic Hamiltonian in the product base of the Dirac
single-particle states at the conduction and valence band edges. Following the
separation of variables we decouple the corresponding energy eigenvalue system
of the first order ODE radial equations rigorously and solve the resulting the
second order ODE self-consistently, using the finite difference method, thus we
determine the energy eigenvalues of the discrete excitonic spectrum and the
corresponding wave functions. We also developed WKB approach to solve the same
spectral problem in semiclassical aproximation for the resulting ODE. We
compare the results for the energy spectrum and the corresponding
eigen-functions forms for WS2 and WSe2 obtained by means of both methods. We
also compare our results for the energy spectrum with other theoretical works
for excitons, and with available experimental data.
