A new quantization rule to the bound state problem in non-relativistic quantum mechanics

In this paper, a new quantization rule to calculate energy spectrum is presented for the bound state problem in non-relativistic quantum mechanics based on the parametric Nikiforov-Uvarov (NU) method. Moreover, it is observed that its final form is conveniently expressed in terms of the original parameters that appear in the general form of the Schrödinger equation. As a result, an analytical formula to the bound state problem is written out explicitly in a straightforward manner without difficulty. The fool-proof nature of the method will appeal to the theorist who requires an analytical solution on the fly. A few special cases arising from this formula are also provided to demonstrate its accuracy.