The Schrödinger equation in integral form is applied to the one-dimensional scattering problem in the case of a narrow potential barrier. Since the kernel can be considered, in a first approximation, separable, an explicit expression for the propagator is found by means of the complementary error function. The problem of a particle confined in a half-space and interacting with a narrow potential barrier is also considered and solved in an approximate way.
Propagator for narrow potential barriers
Paolo Moretti
2005
Abstract
The Schrödinger equation in integral form is applied to the one-dimensional scattering problem in the case of a narrow potential barrier. Since the kernel can be considered, in a first approximation, separable, an explicit expression for the propagator is found by means of the complementary error function. The problem of a particle confined in a half-space and interacting with a narrow potential barrier is also considered and solved in an approximate way.File in questo prodotto:
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