Relation between Poisson and Schrödinger equation in one dimension

Details Relation between Poisson and Schrödinger equation in one dimension Relation between Poisson and Schrödinger equation in one dimension

2011-12-08

arxiv.org/abs/1112.1905v1

Physics

Quantum Physics

Submitted to American Journal of Physics

Scientific paper

The relation between the Poisson and Schr\"odinger equation in one dimension is obtained through a simple transformation. It is pointed out that this analogy between both equations can be only applied for potentials that involve a combination of attractive and repulsive delta function potentials. This relationship enables us to use elementary electrostatic results to find the exact solution of the associated quantum bound state problem in one dimension. Particularly, the result shows that it is possible to trap a single electron in a one dimensional ionic crystal.

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