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

[摘要] 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.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Physics