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arXiv · 0711.0599

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

Djamil Bouaziz·Michel Bawin
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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.

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Djamil Bouaziz, Michel Bawin. 2007-11-05. Regularization of the Singular Inverse Square Potential in Quantum Mechanics with a Minimal length. https://doi.org/10.1103/physreva.76.032112

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