Rayleigh-Schrodinger Perturbation Theory through Second Order

1 Rayleigh-Schrodinger Perturbation Theory though Second Order. - Let 

In order to develop a perturbation series for the systematic correction of the solutions of the zero-order problem, put 

Hi is termed the perturbation operator and X the perturbation parameter. As X is increased from zero to xuiity, equation (3) interpolates between the zero-order hamiltonian appearing in equation (2) and the perturbed hamiltonian appearing in equation (1). 

Consider the case of a single perturbation. Hi, and a non-degenerate reference 

Since the eigenvalue, ,(1), in equation (5) is assumed to be a continuous function of 1, a power series expansion can be made 

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Fig. 11. The spectra for obtained with the bare G-matrix (//ifV) and Rayleigh-Schrodinger perturbation theory through second-order in the G-matrix (WifV). All three potentials have been employed. Energies in MeV.

One of the basic computational methods for the correlation energy is the MP2 method, which gives the result correct through the second order of the Rayleigh-Schrodinger perturbation theory (with respect to energy). 

Fig. 8. Theoretical and experimental low-lying spectrum for 0 obtained with the Bonn A potential defined in Table A.l of Ref. [7], using both a HO basis and a BHF basis. The terms H f, and denote the effective interaction through first, second and third order in Rayleigh-Schrodinger (RS) perturbation theory. All energies in MeV. Taken from Ref. [53].

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