372(5): Complete Set of equations for ECE2 Relativistic Quantum Mechanics: 1) 2D

This note gives the complete set of equations available for 2D relativistic quantum mechanics using plane polar coordinates. It can be seen that there are enough equations to solve the problem completely, to find all the wavefunctions and energy levels. A computation scheme is suggested. The next note will extend this method to the relativistic H atom, using spherical polar coordinates in 3D. In both 2D and 3D there will be fine structure splitting. This does not occur on the non relativistic level as is well known. Having set the groundwork the method can be extended to the helium atom and eventually to the whole of computational quantum chemistry. It is a new ab initio method without use of perturbation theory or any approximation. It makes use of the ECE2 hamiltonian and lagrangian.


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