Non-Hermitian Rayleigh-Schrödinger Perturbation Theory

The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems

Numerical Evidence that the Perturbation Expansion for a Non-Hermitian PT -Symmetric Hamiltonian is Stieltjes

Recently, several studies of non-Hermitian Hamiltonians having PT symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling pertur...

Pseudoinverse Formulation of Rayleigh-schrödinger Perturbation Theory for the Symmetric Matrix Eigenvalue Problem

A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon theMoore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrixtheoretic formulation of this procedure, it also pro...

New Version of the Rayleigh–Schrödinger Perturbation Theory: Examples

It has been shown in our preceding papers that the linear dependence of the perturbation wave functions on the perturbation energies makes possible to calculate the exact perturbation energies from the values of the perturbation wave functions corresponding to arbitrarily chosen trial perturbation energies. The resulting version of the perturbation theory is very simple and can be used at large...

Rayleigh-Schrödinger-Goldstone variational perturbation theory for many fermion systems

We present a Rayleigh-Schrödinger-Goldstone perturbation formalism for many fermion systems. Based on this formalism, variational perturbation scheme which goes beyond the Gaussian approximation is developed. In order to go beyond the Gaussian approximation, we identify a parent Hamiltonian which has an effective Gaussian vacuum as a variational solution and carry out further perturbation with ...