Regularized Green's Function for the Inverse Square Potential

Abstract

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.

10 pages. The final section was expanded

References in corpus (3)

• Singular Potentials and Limit Cycles
• Renormalization of the Inverse Square Potential
• Quantum Anomaly in Molecular Physics

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