A Perturbative Approach in the Minimal Length of Quantum Mechanics

Year 2019, Volume: 6 , 148 - 150, 25.07.2019

Bekir Can Lutfuoglu

Abstract

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.  

Keywords

Schrödinger equation , Generalized uncertainty principle , Perturbation theory

References

• Eshghi, M., Sever, R. & Ukhdair, S.M.. (2019). Thermal and optical properties of two molecular potentials. Eur.Phys. J. Plus, 134, 155. Chung, W.S. & Hassanabadi, H.. (2019). A new higher order GUP: one dimensional quantum system. Eur. Phys. J. C, 79, 213. Villalpando, C. & Modak, S.K.. (2019). Minimal length effect on the broadening of free wave packets and its physical implications. Phys. Rev. D, 100, 052101. Bosso, P. & Obregon, O.. (2019). Quantum cosmology and the Generalized Uncertainty Principle. http://arxiv.org/pdf/1904.06343. Xiang, L., Ling, Y., Shen, Y.-G., Liu, C.-Z., He, H.-S. & Xu, L.-F.. (2018). Generalized uncertainty principles, effective Newton constant and the regular black hole. Ann. Phys., 396, 334. Hassanabadi, H., Zarrinkamar, S. & Maghsoodi, E.. (2012). Scattering states of Woods-Saxon interaction in minimal length quantum mechanics. Phys. Lett. B, 718, 678. Flügge, S.. (1974). Pratical Quantum Mechanics. Berlin: Spinger.