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

Version 2.6, authors: Ilya Kuprov