The exact methods for solving partial differential equations are always preferred because they
present the solution is exact, and do not have any limitations to use. Nevertheless, sometimes we must resort
to the analytical approximate and numerical methods due to limitations of exact solvers. This article aims to
examine the β-derivative of Schr¨odinger equation in exact approach point of view. To this end, we obtain some
novel optical solutions of the equation via the so-called generalized exponential rational function method. To the
best of our knowledge the technique has never been tested for the considered equation in the literature. These
solutions might be useful in mathematical physics, applied mathematics and engineering fields. The employed
technique in this paper may have a great significance applications while handling the other nonlinear partial
differential equations.