vvpert.m

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

Syntax

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

Parameters

    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, acomm.m, arnoldi.m, atranspose.m, aux_mat.m, binpack.m, cheap_norm.m, cheb_coeff.m, clean_up.m, dirdiff.m, eigenfields.m, expdrop.m, expmint.m, expmint2.m, fftdiff.m, fourdif.m, fourlap.m, frob_chop.m, gaussfun.m, hdot.m, herm_spline.m, jacobianest.m, keep_rank.m, krondelta.m, kronm_new.m, logfactorial.m, lorentzcon.m, lorentzfun.m, md5_hash.m, mprealloc.m, remncomm.m, remtrace.m, rspt_eig.m, snormpdf.m, svd_shrink.m, tikhoind.m, tikhonov.m, trapdiff.m, unit_oper.m, unit_state.m, Kernel_utilities

Version 2.6, authors: Ilya Kuprov