Generalized uncertainty principle and the solution limits of the Schrödinger equation due to attenuated eigenfunction

General Relativity, quantum gravity, black hole physics, and string theory all indicate the possibility of the existence of a minimal observable length in the order of Planck length. This notice and others lead to modifying the Heisenberg uncertainty principle to be the Generalized Uncertainty Principle (GUP), as illustrated in many literatures. While the base of quantum mechanics, the Schrödinger equation, did not show this principle, it was used to solve many problems without indicating the limits of their solutions. Here, in this study, some consequences of GUP in the quantum mechanics spirit were presented in one of the most well-known quantum problems: a particle in a one-dimensional box. The study shows a suggested term to be added to the Schrödinger equation, which is derived from an attenuated wavefunction and describes the particle dimension as well as its wave nature according to a minimal length. This concept can be used to solve high-energy physics problems and black hole problems, besides Hawking radiation.