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Normalizable Wave Functions for Bound States and Resonances in S-Matrix Theory

Y. S. Kim*

Kashyap V. Vasavada

  • Center for Theoretical Physics, Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742

  • Department of Physics, Indiana University—Purdue University at Indianapolis, Indiana 46205

  • *Work supported in part by the National Science Foundation under Grant No. NSF GP 8748.
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Phys. Rev. D 5, 1002 – Published 15 February, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.1002

Abstract

Normalizable wave functions are constructed for bound states and resonances from the S-matrix quantities. The bound-state wave function is of the Schrödinger type. The Schrödinger equation does not give normalizable wave functions for resonances. Thus the resonance wave function is of the non-Schrödinger type. An S-matrix model is constructed to generate the desired resonance wave function. The manner in which this model departs from the conventional Schrödinger picture is discussed in detail. This S-matrix model is then applied to the P-wave two-pion system with a satisfactory numerical result for the ρ-meson radius.

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Phys. Rev. D 5, 1002– Published 15 February, 1972
  • Received 25 January 1971

© 1972 American Physical Society

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