The Landau quantization space is based on the respective motion of the electron and hole in a magnetic field and can provide a new route to understand the bound exciton behaviors observed in the experiments. In this paper, we study the two-dimensional exciton properties of monolayer ${\mathrm{WSe}}_2$ in both real space and Landau quantization space. Focusing on the excitons of zero center-of-mass momentum, we calculate the energy spectrum in both spaces, with the results agreeing well with each other. We then obtain the diamagnetic coefficients and root-mean-square radius, which are consistent with the available $s$ state data in the experiments. More importantly, in the exciton state $nl$, we find that the dominant electron-hole pair component may shift with the magnetic field and the Coulomb interactions, and reveal that the magnetic field will drive the dominant component to the free electron-hole pair $\{n_e=n+l-1,n_h=n-1\}$, whereas the Coulomb interactions drives it to the pair of the lower index.

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• Excitons
• Landau levels
• Transition metal dichalcogenides
• Electron-correlation calculations