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The Path Integral for the Kepler Problem on the Pseudosphere

Feb, 1990
16 pages
Published in:
  • Annals Phys. 204 (1990) 208-222
DOI:
Report number:
  • IMPERIAL-TP/89-90/14
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Abstract: (Elsevier)
The path integral for the generalized Kepler problem on the pseudosphere is calculated. As the generalized Kepler problem we describe the potential problem V(α) = −( Ze 2 R )( coth α−1) (α>0, R -curvature) on the D -dimensional pseudosphere, whereas for the genuine Kepler problem this feature of the potential is only true for the four-dimensional pseudosphere. Energy spectrum and wave-functions are explicitly calculated. The result is compared with the flat-space limit (i.e., R → ∞) and with the free motion on the pseudosphere. The application of the result of the path integral solution of the Manning-Rosen potential plays a crucial role in the calculation.
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