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

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

2007-11-05

arxiv.org/abs/0711.0599v1

Phys.Rev.A76:032112,2007

Physics

Quantum Physics

30 pages, 3 figures

Scientific paper

10.1103/PhysRevA.76.032112

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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