  The electronic and structural properties of excitons and trions in monolayer
transition metal dichalcogenides are investigated using both a multiband and a
single-band model. In the multiband model we construct the excitonic
Hamiltonian in the product base of the single-particle states at the conduction
and valence band edges. We decouple the corresponding energy eigenvalue
equation and solve the resulting differential equation self-consistently, using
the finite element method (FEM), to determine the energy eigenvalues and the
wave functions. As a comparison, we also consider the simple single-band model
which is often used in numerical studies. We solve the energy eigenvalue
equation using the FEM as well as with the stochastic variational method (SVM)
in which a variational wave function is expanded in a basis of a large number
of correlated Gaussians. We find good agreement between the results of both
methods, as well as with other theoretical works for excitons, and we also
compare with available experimental data. For trions the agreement between both
methods is not as good due to our neglect of angular correlations when using
the FEM. Finally, when comparing the two models, we see that the presence of
the valence bands in the mutiband model leads to differences with the
single-band model when (interband) interactions are strong.
