2010/03/14 by R. Ducharme, Robert J. Ducharme, Ducharme, Robert J.
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Various Chemistry Research Topics #quant-ph
paper · pdf · doi:10.48550/arxiv.1003.2758
8 pages
arxiv created 2010/03/14 · openalex publication_date 2010/03/14 · arxiv updated 2010/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In a recent paper, it has been shown the Schrödinger 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 Schrödinger equation for the hydrogen atom. This approach has two interesting features. Firstly, it eliminates potential fields from the Schrödinger 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.