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Generation of new classes of exactly solvable potentials

Exact analytic solutions of the Schrödinger equation are obtained for the classes of newly constructed hyperbolic type of potentials which are generated from the Eckart and trigonometric Rosen–Morse (tRM) potentials as input reference potentials via the extended transformation method. A set of quantized energy spectra of the bound states and the corresponding wavefunctions of the constructed potentials are obtained. We also focus on the Romanovski polynomial, which is a family of real orthogonal polynomials and is required to present exact solutions of tRM potential.