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Conformal Transformation of the Schr\"{o}dinger Equation for Central Potential Problems in Three-Dimensions by Ducharme, Robert J. is a scholarly article available to read on EtoBox.

What is Conformal Transformation of the Schr\"{o}dinger Equation for Central Potential Problems in Three-Dimensions about?

In a recent paper, it has been shown the Schr\"{o}dinger equation for the three-dimensional harmonic oscillator can be simplified through the use of an isometric conformal transformation. Here, it is demonstrated that the same transformation technique is also applicable to the Schr\"{o}dinger equation for the hydrogen atom. This approach has two interesting features. Firstly, it eliminates potential fields from the Schr\"{o}dinger equation. The Coulomb and harmonic binding terms are instead represented as imaginary parts of complex time. Secondly, the method leads to a general relationship between potential energy and ground state energy that encompasses both the hydrogen atom and the harmonic oscillator as special cases.

Author

Ducharme, Robert J.

Published

2010

Language

EN