β Scribed by Y Tikochinsky
No coin nor oath required. For personal study only.
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 onedimensional 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.
π SIMILAR VOLUMES
For the description of inelastic scattering a new form of close coupled equations is proposed. The coupled equations considered in our previous study are normalized. The solutions for the normalized amplitudes do not contain exponentially large terms. The normalization removes the last problem in th
## Abstract We consider the wholeβline inverse scattering problem for SturmβLiouville equations which have constant coefficients on a halfβline. Since in this case the reflection coefficient determines a WeylβTitchmarsh __m__βfunction, it determines the coefficients up to some simple Liouville tran