372(1): The Fundamental Wave Equation of Lagrangian Quantum Mechanics

This fundamental wave equation is made up of Eqs. (29) and (30), which give the radial wavefunctions in terms of the Bohr radius. The angular wavefunctions are the spherical harmonics. The three dimensional ellipse (8) of Lagrangian quantum mechanics is defined by the quantized half right latitude (21) and the quantized eccentricity (22). These equations agree with the results of previous work of the UFT series, notably UFT266 and UFT267. These results are for the H atom with Coulomb potential (7) describing the interaction of one electron with one proton. In general there are many electons and many protons (and also neutrons), and this method can be extended to describe the general atom or molecule, building up a new computational quantum chemistry. In the well known hamiltonian approach to quantum chemistry, only the H atom is analytical. All other atoms and molecules are developed with approximations or by computation. As Horst showed in UFT371, the Lagrangian method is much simpler than the Hamiltonian method for the H atom, and the same is true for other atoms and molecules.


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