A Unified Treatment of Quasi-Exactly Solvable Potentials II: Eckart Type Potentials

This work continues to study the set of quasi exactly solvable potentials related to the Eckart, Hult\'{e}n, Rosen-Morse, Coulomb and the harmonic oscillator potentials. We solve the Schr\"{o}dinger equation for each potential and obtain the eigenvalues and eigenstates in terms of the orthogonal polynomials. We present a unified approach to obtain the potentials from each other by suitable change of variables.