Operator Calculus and the Solution of the Equations of Quantum Dynamics

A formal calculus is developed which includes the Born and Jordan matrix dynamics, and also the remarkable quantum condition of Schroedinger. A method for the calculation of the matrices which is in close analogy to the classical Hamilton-Jacobi method of solving dynamical problems is explained. These results have been obtained independently by E. Schroedinger [Ann. d. Physik. 79, 734 (1926)].