Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length

Abstract

We study the problem of the attractive inverse square potential in quantum mechanics with a generalized uncertainty relation. Using the momentum representation, we show that this potential is regular in this framework. We solve analytically the s-wave bound states equation in terms of Heun's functions. We discuss in detail the bound states spectrum for a specific form of the generalized uncertainty relation. The minimal length may be interpreted as characterizing the dimension of the system.

30 pages, 3 figures

References in corpus (5)

• Hydrogen-atom spectrum under a minimal-length hypothesis
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• Perturbation hydrogen-atom spectrum in deformed space with minimal length
• Casimir Effect in the Presence of Minimal Lengths
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length

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