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Volumn 85, Issue 8, 2000, Pages 1590-1593

Renormalization of the inverse square potential

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DEGREES OF FREEDOM (MECHANICS); FUNCTIONS; GROUND STATE; INVARIANCE; INVERSE PROBLEMS; PHASE SHIFT;

EID: 0034251289     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.1590     Document Type: Article
Times cited : (152)

References (43)
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    • Momentum-space analyses of the two-dimensional δ-function potential include C. Thorn, Phys. Rev. D 19, 639 (1979); K. Huang, Quarks, Leptons, and Gauge Fields (World Scientific, Singapore, 1982), Secs. 10.7 and 10.8; R. Jackiw, in M. A. B. Bég Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991).
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    • Momentum-space analyses of the two-dimensional δ-function potential include C. Thorn, Phys. Rev. D 19, 639 (1979); K. Huang, Quarks, Leptons, and Gauge Fields (World Scientific, Singapore, 1982), Secs. 10.7 and 10.8; R. Jackiw, in M. A. B. Bég Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991).
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    • Momentum-space analyses of the two-dimensional δ-function potential include C. Thorn, Phys. Rev. D 19, 639 (1979); K. Huang, Quarks, Leptons, and Gauge Fields (World Scientific, Singapore, 1982), Secs. 10.7 and 10.8; R. Jackiw, in M. A. B. Bég Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991).
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    • As an alternative, the momentum-space scheme of Ref. [14] is applied numerically to a related problem (inverse square potential with exponential screening) in C. F. de Araujo, Jr., L. Tomio, S. K. Adhikari, and T. Frederico, J. Phys. A 30, 4687 (1997).
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    • note
    • Incidentally, our theory in D dimensions has a two-dimensional appearance, due to dimensional transmutation. This is in sharp contrast with the behavior of the solutions of the wave equation and of the free-particle Schrödinger equation. See also Eq. (10).
  • 43
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    • note
    • The present solution of the inverse square potential (with 1 = 0) applies to the radial part of the wave function under a dipole potential; the angular part can be dealt with by using the method of Ref. [10].


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