Lagrangian Functions Which Determine a Symmetrical Tensor by Schrodinger's Rule

Citation

Hicks, Hervey Crandall (1928) Lagrangian Functions Which Determine a Symmetrical Tensor by Schrodinger's Rule. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/EKPF-YT05. https://resolver.caltech.edu/CaltechETD:etd-02282005-140719

Abstract

The choice of a Lagrangian function to be used in a variational principle may be limited by the condition that the tensor derived from it by Schrodinger’s rule shall be symmetrical. To meet this condition the function must satisfy a certain set of partial differential equations. Particular and general solutions of these equations are found in various cases—according as the function is restricted to depend (A) only on the components of a vector, (B) only on their first derivatives, or (C) on both; and according to the number of dimensions of the vector. Methods of obtaining such solutions, and of proving their independence or of finding the relations between them, are discussed.

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