Duality between Poisson and Schr\"odinger equations in three dimensions
- URL: http://arxiv.org/abs/2107.04669v1
- Date: Fri, 25 Jun 2021 18:46:45 GMT
- Title: Duality between Poisson and Schr\"odinger equations in three dimensions
- Authors: G. Gonzalez
- Abstract summary: A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world is studied.
It is demonstrated that the same transformation technique is also applicable to the s-wave Schr"odinger equation in three dimensions for central potentials.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A duality between an electrostatic problem in a three dimensional world and a
quantum mechanical problem in a one dimensional world which allows one to
obtain the ground state solution of the Schr\"odinger equation by using
electrostatic results is generalized to three dimensions. Here, it is
demonstrated that the same transformation technique is also applicable to the
s-wave Schr\"odinger equation in three dimensions for central potentials. This
approach leads to a general relationship between the electrostatic potential
and the s-wave function and the electric energy density to the quantum
mechanical energy.
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