Physics – Quantum Physics
Scientific paper
2002-11-28
Physics
Quantum Physics
Revtex, 9 pages, 3 EPS figures. To be published in PRA
Scientific paper
10.1103/PhysRevA.66.062712
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of $N$ general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.
Cheng Bin Kang
da Luz Marcos G. E.
Schmidt Alexandre G. M.
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