Abstract
For the class of potentials vanishing beyond a certain point we have derived a new dispersion formula in which the scattering matrix S(k) is written as the ratio of two conditionally convergent partial fraction sums. The numerator displays the poles of S(k) at the complex eigenvalues kn and the denominator displays poles at -kn, the zeros of S(k). The expression is manifestly unitary and remains so when an approximation depending only on a finite number of poles is made. Besides the S-wave theory, higher-wave scattering is treated, and among particular illustrations is a generalization to higher waves of the effective range approximation.
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