The properties of the 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 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 a WKB approach to solve the same spectral problem in semiclassical approximation for the resulting ODE. We compare the results for the energy spectrum and the corresponding eigen-function 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.

使用多波段模型研究了单层过渡金属二硫属化物中激子的能谱特性。在多带模型中，我们在导带和价带边缘的狄拉克单粒子态的乘积基中使用激子哈密顿量。在变量分离之后，我们严格解耦一阶 ODE 径向方程的相应能量特征值系统，并使用有限差分方法自洽求解得到的二阶 ODE，从而确定离散激子的能量特征值谱和相应的波函数。我们还开发了一种 WKB 方法来解决所得 ODE 的半经典近似中的相同谱问题。₂和 WSe ₂通过这两种方法获得。我们还将我们的能谱结果与激子的其他理论工作以及可用的实验数据进行了比较。