Exact solution of the 't Hooft equation in the limit of heavy quarks with unequal masses

We consider the 't Hooft equation for bound states in the two-dimensional quantum chromodynamics in the limit of an infinite number of colors. In the case of quarks with unequal masses tending to infinity, we obtain an approximation to the low-energy part of the spectrum and the corresponding wave functions. We show that as in the case of equal masses, the 't Hooft equation in the first approximation reduces to the Schrödinger equation with a linear potential, i.e., to the equation for a particle in a "triangular" potential well. We also discuss the possibility of obtaining corrections to this approximation.