Abstract
The potential energy surface of a molecule can be decomposed into equipotential hypersurfaces of the level sets. It is a foliation. The main result is that the contours are the wave fronts of a certain hyperbolic partial differential equation, a wave equation. It is connected with the gradient lines, as well as with a corresponding eikonal equation. The energy seen as an additional coordinate plays the central role in this treatment. A solution of the wave equation can be a sharp front in the form of a delta distribution. We discuss a general Huygens’ principle: there is no wake of the wave solution in every dimension.
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Acknowledgments
Financial support from the Spanish Ministerio de Ciencia e Innovación, DGI project CTQ2011-22505 and, in part from the Generalitat de Catalunya projects 2009SGR-1472 is fully acknowledged. It is a pleasure to thank Prof. R. Schimming for a helpful discussion to Ref. [13]. We thank M. Belger for a careful reading of the manuscript.
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Quapp, W., Bofill, J.M. Level sets as progressing waves: an example for wake-free waves in every dimension. J Math Chem 52, 654–664 (2014). https://doi.org/10.1007/s10910-013-0286-9
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DOI: https://doi.org/10.1007/s10910-013-0286-9