Variable amplitude equations for one-dimensional scattering |
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Authors: | Y Tikochinsky |
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Affiliation: | Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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Abstract: | Nonlinear first-order equations, similar to Calogero's equations, are derived for the forward and backward one-dimensional scattering amplitudes. In particular, the even potential case yields two uncoupled equations for the even and odd parity phase shifts. The present approach provides a fast and accurate means for the numerical solution of one-dimensional scattering problems. It also has many analytic merits, some of which are discussed. The connection between one-dimensional and three-dimensional high-energy scattering is reviewed. It is demonstrated that in the one-dimensional case, a slightly modified WKB wavefunction provides an excellent approximation to the exact wavefunction in the shortwave limit. In this limit, additivity of phase shifts for nonoverlapping static potentials is satisfied. |
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