By using Formula method for bound state problems, we have obtained the approximate analytical solution of the radial Schrӧdinger equation for Varshni potential model. The energy eigenvalues and the corresponding eigenfunctions are calculated in closed forms. In the process, eigen values for 1, 1, 2, a b a b = = = − = − and 1, 2 b a = − = − for 2 , 3 ,3 , 4 p p d p and 4 f states with three different values of the potential range were generated using the Varshni potential. Special cases of the potential are equally studied. Some numerical results have been presented which showed a good agreement with previous results obtained from another method.The study of exactly solvable problem has attracted much attention in theoretical physics since the development of quantum mechanics. For instance, the solutions of the non-relativistic Schrӧdinger equation for a hydrogen atom and a harmonic oscillator in three dimensions represent two typical examples in quantum mechanics (Schiff, 1955;Landau and Lifshitz, 1977). There are few traditional techniques or methods used to solve second-order differential equation in order to obtain the solutions of the quantum systems. These methods include Nikiforov-Uvarov method (Ebomwonyi et al., 2017; Ikot et al., 2015; Onate and Idiodi, 2015; Hamzavi and Ikhdair, 2012), asymptotic iteration method (Bayrak et al., 2007; Falaye et al., 2013; Bayrak and Boztosun, 2007; Ateser et al., 2007), supersymmetry shape invariance and solvable potential (Zarrinkamar et al., 2010; Jia et al., 2011; Hassanabadi, 2011; Onate et al., 2017), factorization method (Onyeaju et al., 2016), new exact quantization rule (Dong and Gonzalez-Cisneros, 2008; Gu et al., 2009) and others. Recently, Falaye et al. (2014) developed the Formula method for bound state problems from asymptotic iteration method. This method seems to be very effective, but the simplification in obtaining the energy equation is somehow technical; hence, resulting in little report on it in literature. This necessitates the present study; and in this paper, we intend to investigate the nonrelativistic Schrödinger equation with the Varshni potential function in the framework of the Formula method for bound state problems. To the best of our knowledge, this is the first time the Schrӧdinger equation is being studied with the Varshni potential function using the Formula method.The Varshni potential function is given as (Varshni, 1957;Oluwadare and Oyewumi, 2017) ( ) , r ab V a r e r δ − = −(1) Where, a and b are the potential strengths, δ is the screening parameter which controls the shape of the potential energy curve and r is the internuclear separation. The Varshni potential function is a short range repulsive potential energy function that plays an important role in both chemical and molecular physics (Varshni, 1957). The potential was used by Kaxiras and Pandey to describe the 2-body energy portion of multi-body condensed matter. This potential is used generally to describe bound states of the interaction of systems and has been applied in both...
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