The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, non singular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.
Propagator for finite range potentials
Ilaria Cacciari;Paolo Moretti
2006
Abstract
The Schroedinger equation in integral form is applied to the one-dimensional scattering problem in the case of a general finite range, non singular potential. A simple expression for the Laplace transform of the transmission propagator is obtained in terms of the associated Fredholm determinant, by means of matrix methods; the particular form of the kernel and the peculiar aspects of the transmission problem play an important role. The application to an array of delta potentials is shown.File in questo prodotto:
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