vvpert.m

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Van Vleck perturbation theory, following Shavitt and Redmon, but excluding the quasi-degenerate split.

Syntax

    [Ep,G]=vvpert(E0,H1,order)

Arguments

    E0    - eigenvalues of H0, a column vector of real 
            numbers

    H1    - perturbation, written in the basis that di-
            agonalises H0

    order - order of perturbation theory to be used, 5
            is the maximum available

Outputs

    Ep    - eigenvalues of H0+H1 to the specified order,
            a column vector of reals, not necessarily 
            sorted in the same way as the input

    G     - Van Vleck transformation generator, such that
            expm(G) is a square unitary matrix with eigen-
            vectors in columns, in the same order as the 
            eigenvalues in Ep

Notes

There must be no degeneracies in H0; H1 must be Hermitian, the theory only converges when norm(H1,2) is much than the smallest energy gap in H0; complexity is linear in the order and cubic in the matrix dimension

See also

rspert.m, Numerical infrastructure


Version 2.6, authors: Ilya Kuprov