Path-integral formulation of scattering theory: Central potentials

Christopher C. Gerry; Vijay A. Singh

doi:10.1103/PhysRevD.21.2979

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Path-integral formulation of scattering theory: Central potentials

Christopher C. Gerry

Vijay A. Singh

Department of Physics, Seton Hall University, South Orange, New Jersey 07079

Physics Department, State University of New York at Albany, 1400 Washington Avenue, Albany, New York 12222

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Phys. Rev. D 21, 2979 – Published 15 May, 1980

DOI: https://doi.org/10.1103/PhysRevD.21.2979

Abstract

We consider central-potential scattering and determine a path-integral representation for the $S$ matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic $S$ matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the $S$ matrix.

References (9)

C. L. Hammer, J. E. Shrauner, and B. De Facio, Phys. Rev. D 18, 373 (1978)
W. B. Campbell, P. Finkler, C. E. Jones, and M. N. Misheloff, Phys. Rev. D 12, 2363 (1975)
D. Peak and A. Inomata, J. Math. Phys. 10, 1422 (1969)
A. Inomata and V. A. Singh, J. Math. Phys. 19, 2318 (1978)
C. C. Gerry and V. A. Singh, Phys. Rev. D 20, 2550 (1979)
G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, England, 1962), 2nd ed., p. 395
E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), 2nd ed., p. 504
L. D. Faddeev, in Methods in Field Theory, edited by Roger Balian and Jean Zinn-Justin (North-Holland, Amsterdam, 1976)
S. F. Edwards and Y. V. Gulyaev, Proc. R. Soc. London A279, 229 (1964)

[c1] C. L. Hammer, J. E. Shrauner, and B. De Facio, Phys. Rev. D 18, 373 (1978)

[c2] W. B. Campbell, P. Finkler, C. E. Jones, and M. N. Misheloff, Phys. Rev. D 12, 2363 (1975)

[c3] D. Peak and A. Inomata, J. Math. Phys. 10, 1422 (1969)

[c4] A. Inomata and V. A. Singh, J. Math. Phys. 19, 2318 (1978)

[c5] C. C. Gerry and V. A. Singh, Phys. Rev. D 20, 2550 (1979)

[c6] G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, England, 1962), 2nd ed., p. 395

[c7] E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), 2nd ed., p. 504

[c8] L. D. Faddeev, in Methods in Field Theory, edited by Roger Balian and Jean Zinn-Justin (North-Holland, Amsterdam, 1976)

[c9] S. F. Edwards and Y. V. Gulyaev, Proc. R. Soc. London A279, 229 (1964)

Physical Review D

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Path-integral formulation of scattering theory: Central potentials

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