In this paper, an entire new approach for quantum mechanics calculation, the non-degenerate ground state steepest descent perturbation theory (SDPT) suggested by Cioslowski is developed and extended for dealing with degenerate ground state problem. Using sysmme-try adapted trial wave ket, the SDPT iteration for different sublevel is independent from each other and improves its eigen energy and wave function step by step. Therefore, the steepest descent perturbation theory can be used to calculate the low symmetry splitting of degenerate ground state and the correlation energy to arbitrary precison. Unlike other perturbation theory, this does not require either infinite summation overlstates or the solution of a set of differential equations, it could be expected wide adaptability in the calculation of energy level perturbation splitting of atoms, molecules and orther many body quantum system.
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