Abstract
It is shown that fundamental properties of kinetic energy determine its operator in wave mechanics almost completely: The part containing differential operators is unequivocally given by the Laplacian calculated for the metric which is defined by the classical kinetic energy. The only remaining ambiguity is an additive scalar function proportional to ħ2. Invariance properties with respect to infinitesimal transformations may reduce the number of coordinates on which this function depends. In certain cases it must be constant.
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Part of a thesis, Heidelberg 1971.
The problem was suggested by Professor K. Dietrich. I thank him as well as Professors K. Hara and J. H. D. Jensen for helpful discussions and Professor K. Dietrich particularly for his critical reading of the manuscript.
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Hofmann, H. On the quantization of a kinetic energy with variable inertia. Z. Physik 250, 14–26 (1972). https://doi.org/10.1007/BF01386889
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DOI: https://doi.org/10.1007/BF01386889