PRINCIPLES OF THE 1ST AND 2ND KIND OF BALANCE IN A VARYING-PARAMETERSMETHOD FOR EIGENVALUE PROBLEMS IN QUANTUM-MECHANICS

In this paper a method for eigenvalue problems in quantum mechanics is developed. Principles of the first and second kinds of balance in a v arying-parameters method take advantage of the standard perturbation t heory and the standard variational principle. According to this method , we not only obtain the best approach for obtaining eigenvalues and w ave functions, but we also determine structures of a quantum system. T he extended Hamiltonian in a varying-parameters method is different fr om a standard Hamiltonian. The parameters are inserted into a Hamilton ian by adding and subtracting appropriate terms which contain the esse ntial parameters. Thus it becomes possible to study the inner structur e of a quantum system by applying principles of balance. In order to i nterpret the physical meanings of balance parameters, several examples are described. Applications are also made to the helium atom, helium- like ions, and the lithium atom. We theoretically predict energies and structure parameters and obtain good agreement with experimental data , especially for high-orbit electrons (clearly this is a character of perturbation theory). It is quite interesting that the theoretical pre dictions of energy levels of parahelium in the S state are lower than the energy levels of orthohelium and that theoretical predictions of s inglet (triplet) states are close to the experimental data of triplet (singlet) states. It would seem that the experimental data of triplet and singlet are reversed. Is that possible?