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Integral equations and the bound-state problem
, R.G. Seyler
Published in
Volume: 48
Issue: 10
Pages: 828 - 833
An integral equation for the s-wave bound-state solution is derived and then solved for a square-well potential. It is shown that the scattering solutions continue to exist at negative energies, and when evaluated at the energy of a bound state these solutions do reduce to the bound-state solution. The bound-state energies of a square-well potential are deduced also from orthogonality considerations. Finally, the existence of bound states for an arbitrary short-range potential is related to the occurrence of zeros of the Jost function or poles of the S matrix for that potential. © 1980, American Association of Physics Teachers. All rights reserved.
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