\begin{document}$ N_c\to \infty $\end{document} limit. We consider two types of hadrons, an exotic "meson" (which is composed of a bosonic quark and a bosonic anti-quark), and an exotic "baryon" (composed of a fermionic quark and a bosonic antiquark). Using the Hamiltonian operator approach, we derive the corresponding bound-state equations for both types of hadrons from the perspectives of the light-front quantization and equal-time quantization, and confirm the known results. We also present a novel diagrammatic derivation for the exotic "meson" bound-state equation in the equal-time quantization. The bound-state equation for the exotic baryons in the equal-time quantization in two-dimensional QCD is new. We also numerically solve various bound-state equations, obtain the hadron spectrum and the bound-state wave functions of the lowest-lying states. We explicitly demonstrate the pattern that as the hadron is boosted to the infinite-momentum frame, the forward-moving bound-state wave function approaches the corresponding light-front wave function."> Solving bound-state equations for scalar and hybrid QCD in two-dimensional spacetime -
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