g 2 Algebra and two-dimensional quasiexactly solvable Hamiltonian related to Poschl–Teller potential

In this article, we write the general form of the quasiexactly solvable Hamiltonian of g ₂ algebra via one special representation in the x–y two-dimensional space. Then, by choosing an appropriate set of coefficients and making a gauge rotation, we show that this Hamiltonian leads to the solvable Poschl–Teller model on an open infinite strip. Finally, we assign g ₂ hidden algebra to the Poschl–Teller potential and obtain its spectrum by using the representation space of g ₂ algebra.