Approximate Ro-Vibrational Spectrum of the Modified Rosen–Morse Molecular Potential Using the Nikiforov–Uvarov Method

In many fields of physics and chemistry, explicit analytical solutions of the fundamental dynamical equations are much valuable for a general understanding of phenomena, e. g. the role played by physical parameters. Two typical examples in quantum mechanics are the exact solutions of the Schrödinger equation (SE) for a hydrogen atom (Coulombic) and for a harmonic oscillator [1 – 3]. The Mie-type and pseudoharmonic potentials are also two exactly solvable potentials [4, 5]. Further, there are many potentials that are exactly solvable for zero angular momentum (i. e. l = 0). However, their analytic exact solutions can not be obtained for l 6= 0, and many authors have used various approximation schemes to solve these problems [6 – 23]. The modified Rosen–Morse potential (also called Scarf II type) [24, 25] is an exponential and anharmonic potential defined by