An-Najah Staff

We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form ofΨ′′(s)+(k1−k2s)s(1−k3s)Ψ′(s)+(As2+Bs+C)s2(1−k3s)2Ψ(s)=0. The two cases where k 3 = 0 andk3≠0are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions2F1(α,β;γ;k3s). In order to show the accuracy of this proposed formula, we resort to obtaining bound state solutions for some existing eigenvalue problems in a rather more simplified way. This method has shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models.