Abstarct: In the last few decades, some gaps in quantum mechanics have led to the proposal of changing its shape. These deformations have been studied with different approaches such as structural deformations, deformation operators, or non-normal potentials. First, we discussed the various motivations for changes in quantum mechanics and briefly discussed some of these changes. We started with a modified formalism for the Dirac potential. In the transformed formalism there is a quantum algebra that when the transformed parameter reaches its limit state, this algebra becomes normal algebra. Deformed formalism or q-deform formalism has been found in different applications in mathematics and physics of nuclei, high energy physics, black hole physics, and cosmic strings. By introducing the transformed delta function, we derived the Dirac equation for fermions in the presence of a scalar and vector potential of the Dirac delta. Then, according to the boundary conditions and the effect of the Dirac delta potential transformed with the parameter q, the scattering mode of the wave function has been examined. In addition, we obtained the reflection and transmission coefficients in the presence of this deformed potential and the effects of the q parameter on these values have been discussed. Another case of transformations is related to the uncertainty principle relationship, which is proposed by various theories, including quantum gravity. These theories predict the existence of a minimum measurable length in the dimensions of the Planck length. Next, we introduced Heisenberg's uncertainty principle and minimum length. Different generalizations of the uncertainty principle have been introduced and called the generalized uncertainty principle (GUP). The effects of GUP on relativistic and non-relativistic problems generally lead to non-linear sentences, which can be solved using different methods. To Examine these effects in the context of non-relativism, we first introduce the generalized Legendre transform and then the modified Hamiltonian baxsed on GUP. By interpreting the momentum in the presence of GUP, we constructed the modified Lagrangian and for some of the presented GUP models, the new equation of motion has been obtained. In the field of relativity, we found a quantum metric correction of the Schwarzschild black hole baxsed on the generalized uncertainty principle (GUP). We considered a massless scalar field with an effective potential obtained baxsed on GUP. Since the Klein-Gordon equation with the scalar field does not have an explicit analytical answer, various methods have been presented for its approximate analytical solution. Obtaining the effective potential numerically, we approximated the effective potential with one of the functions proposed in the literature. Then, the phase change of the scattering wave function, scattering cross-sections, reflection, and transmission coefficients have been investigated. In the following, we proposed a new potential for effective potential approximation. By comparing the results obtained from the proposed function and the previous method, we analyzed the accuracy of the proposed function with numerical results. Another theory that can be referred to as a deformed structure is the non-commutative space, which assumes that the displacement of the location components is an asymmetric tensor, which can be zero in a special case. According to this theory, two different approaches for an alternative to displacement noncommutativity are presented in black hole physics. One of them is the deformation caused by displacement on the black hole metric and another method without any change in the metric and is only considered as an effect on the mass source. We started with the first approach and investigated the effect of noncommutativity on various aspects of Schwarzschild black hole physics. We investigated the thermodynamic properties of the black hole, then by three different methods, quasi-normal modes of the wave function were examined. Moreover, the effect of noncommutativity on the scattering cross-section, shadow radius, and gravitational convergence of the black hole was discussed. On the other hand, this approach led us to the conclusion that this method can be considered equivalent to a deformation in the mass of the black hole. To investigate this proposal, we have also performed the above calculations with the modified mass approach. The results of temperature and other thermodynamic values of the two methods have been compared. Also, with the deformed mass approach, other properties of scattering wave function such as quasinormal modes, absorption cross sections, and the geodesic of a Schwarzschild black hole in the presence of noncommutativity have been analyzed.