In this paper, we study the quasi-exactly solvable problems for two dimensional quantum systems. By using the Bethe ansatz method, we obtain the general form of the quasi-exactly solvable potential. Then, we present several examples to give the specific forms of quasi-exactly solvable potentials. In the examples, some physical models of quasi-exactly solvable problems are re-exhibited.
03.65.Ge Solutions of wave equations: bound states
$^1$College of Science, Civil Aviation University of China, Tianjin 300300, China
$^2$State grid anping county electric power supply company, Hengshui anping county 053600, China
$^3$College of Gemology and Material Technics, Shijiazhuang University of Economics, Shijiazhuang 050031, China