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The properties of energy spectrum of excitons in monolayer transition metaldichalcogenides are investigated using a multiband model. In the multibandmodel we use the excitonic Hamiltonian in the product base of the Diracsingle-particle states at the conduction and valence band edges. Following theseparation of variables we decouple the corresponding energy eigenvalue systemof the first order ODE radial equations rigorously and solve the resulting thesecond order ODE self-consistently, using the finite difference method, thus wedetermine the energy eigenvalues of the discrete excitonic spectrum and thecorresponding wave functions. We also developed WKB approach to solve the samespectral problem in semiclassical aproximation for the resulting ODE. Wecompare the results for the energy spectrum and the correspondingeigen-functions forms for WS2 and WSe2 obtained by means of both methods. Wealso compare our results for the energy spectrum with other theoretical worksfor excitons, and with available experimental data.

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles