A Perturbative Approach in the Minimal Length of Quantum Mechanics

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

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