Perturbation Theory of Product Hamiltonians through Fourth Order

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Abstract
Expressions are derived through fourth order in a V representation for the eigenvalues and off-diagonal elements of Hamiltonians expressible as sums of products of operators from two Hilbert spaces (V and R), H=0HV+0HR+ ∑ p(HVHR)p. The zeroth order Hamiltonian is assumed separable, and the eigenvalue differences in the V space are assumed to be an order of magnitude larger than the eigenvalue differences in the R space. The method involves successive contact transformations chosen to yield results in terms of matrix elements in the V space and operators in the R space. The technique allows for the exclusion of interactions between resonant states in the V space for subsequent numerical diagonalization.

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