Abstract
The potential term in the Schrödinger equation can be eliminated by means of a conformal transformation, reducing it to an equation for a free particle in a conformally related fictitious configuration space. A conformal transformation can also be applied to the Klein–Gordon equation, which is reduced to an equation for a free massless field in an appropriate (conformally related) spacetime. These procedures arise from the observation that the Jacobi form of the least action principle and the Hamilton–Jacobi equation of classical non-relativistic mechanics can be interpreted in terms of conformal transformations.
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Faraoni, V., Faraoni, D.M. Elimination of the Potential from the Schrödinger and Klein–Gordon Equations by Means of Conformal Transformations. Foundations of Physics 32, 773–788 (2002). https://doi.org/10.1023/A:1016522910236
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DOI: https://doi.org/10.1023/A:1016522910236