On the quantization of a kinetic energy with variable inertia
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.