@article{article_616182, title={A Perturbative Approach in the Minimal Length of Quantum Mechanics}, journal={The Eurasia Proceedings of Science Technology Engineering and Mathematics}, volume={6}, pages={148–150}, year={2019}, author={Lutfuoglu, Bekir Can}, keywords={Schrödinger equation,Generalized uncertainty principle,Perturbation theory}, abstract={<p> <span style="font-size: 10pt; line-height: 115%; font-family: "Times New Roman", serif;">There are many pieces of evidence for a minimal length of the order of Planck length in the problems in quantum gravity, string theory, and black-hole physics etc. Existing of such a minimal length description modifies the traditional Heisenberg uncertainty principle. The novel form is called "the generalized uncertainty principle" in the jargon. Such a deformation in the uncertainty relation changes the corresponding wave equation. The latter Schrodinger equation is now no more a second-order differential equation. Consequently, this causes a great difficulty to obtain the analytic solutions. In this study, we propose a perturbative approach to the bound state solutions of the Woods-Saxon potential in the Schrodinger equation by adopting the minimal length. Here, we take the extra term as a perturbative term to the Hamiltonian. Then, we calculate the first order corrections of the energy spectrum for a confined particle in a well by a Woods-Saxon potential energy. </span> <span style="font-size:10.5pt;line-height: 115%;font-family:"Times New Roman","serif";mso-fareast-font-family:Calibri; color:#333333;background:#F9F9F9;mso-ansi-language:EN-US;mso-fareast-language: AR-SA;mso-bidi-language:AR-SA">   </span> <br> </p>}, publisher={ISRES Publishing}