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Author Rosenberg, L. ♦ Spruch, L.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword PHYSICS ♦ EIGENVALUES ♦ ENERGY ♦ SCATTERING
Abstract It was recently shown that rigorous upper bounds on scattering lengths ran be obtained by adding to the Kohn variational expression certain integrals involving approximate wave functions for each of the negative-energy states. For potentials which vanish identically beyond a certain point, it is possible to extend the methed to positive-energy scattering; one obtains upper bounds on (-k cot?)/sup -1/, where ? is the phase shift. In addition to the negative-energy states one must consider a finite number of states with positive energies lying below the scattering energy. The states in this associated energy eigenvalue problem are defined by the imposition of certain boundary conditions on the wave functions. A second approach, involving an associated potential-strength eigenvalue problem, is used. The second method includes the first as a special case and, more significantly, can be extended to scattering by compound systems. If some states are not accounted for, a bound on cot? is not obtained; nevertheless it is still possible to obtain a rigorous lower bound on ?. Upper bounds on ? may also be obtained, but in a way which is probably not very useful for many-bedy scattering problems. (auth)
ISSN 0031899X
Educational Use Research
Learning Resource Type Article
Publisher Date 1960-10-15
Publisher Department New York Univ., New York
Journal Physical Review
Volume Number 120
Technical Publication No. CX-49
Organization New York Univ., New York


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