Journal of Physics: Theories and Applications E-ISSN: 2549-7324 / P-ISSN: 2549-7316 J. Phys.: Theor. Appl. Vol. 5 No. 2 (2021) 56-68 doi: 10.20961/jphystheor-appl.v5i2.55328 56 Study of Klein Gordon Equation with Minimum Length Effect for Woods-Saxon Potetial using Nikiforov-Uvarov Functional Analysis W Andaresta 1 , A Suparmi 1* , C Cari 1 1 Departmenet of Physics, Faculty of Math and Natural Science, University of Sebelas Maret, Jl. Ir. Sutami 36 A, Kentingan, Surakarta 57126, Indonesia email: soeparmi@staff.uns.ac.id Received 20 July 2021, Revised 20 August 2021, Published 30 September 2021 Abstract. The equation of Klein-Gordon for Woods-Saxon potential was discussed in the minimal length effect. We have found the completion of this equation using an approximation by suggesting a new wave function. The Klein-Gordon equation in the minimal-length formalism for the Woods-Saxon potential is reduced to the form of the Schrodinger-like equation. Then the equation was accomplished by Nikiforov-Uvarov Functional Analysis (NUFA) with Pekeris approximation. This technique is applied to gain the radial eigensolutions with chosen exponential-type potential models. The method of NUFA is more compatible by eliminating vanishing the strict mathematical manipulations found in other methods. The energy calculation results showed that angular momentum, quantum number, minimum length parameter, and atomic mass influenced it. The higher the quantum number and angular momentum, the lower the energy. In contrast to the minimum length, the energy spectrum will increase in value when the minimum length parameter is enlarged. An increase in atomic mass also causes energy to increase as the quantum number and angular momentum are held constant. Keywords: Klein-Gordon equation, minimal length effect, Woods-Saxon potential, Nikiforov-Uvarov Functional Analysis (NUFA) method. 1. Introduction The equation of Klein-Gordon or Lorentz covariance equation belongs to the relativistic wave equation. This second order equation in time and space has a negative energy solution and a negative probability. This matter made the Klein-Gordon equation not immediately popular the year it was introduced. Accordingly, the Klein-Gordon equation is known for describing the relativistic particles dynamics with zero spin (Lutfuoglu et al., 2018). The Klein-Gordon equation with zero spin is very important in quantum mechanics for explaining complete information about quantum systems. This information can be obtained from the wave function (Badalov et al., 2010). In 2015, the equation of Klein-Gordon was accomplished for the Woods-Saxon potential (Olgar & Mutaf, 2015). Subsequently, thi equation also has been solved for Eckart potential [4], Kratzer potential [5], and hyperbolic potential (Onate et al., 2017).