Linear representation of energy-dependent Hamiltonians
Quantum Physics
2007-05-23 v2
Abstract
Effective (i.e., subspace-constrained) Hamiltonians become, by construction, energy-dependent while all the energy-dependent forces prove non-linear because the energy itself is merely an eigenvalue of the Hamiltonian H. One of the most natural resolutions of such a puzzle is proposed via an introduction of teh two separate linear representatives of the respective right and left action of H=H(E). Both the new energy-independent operators are non-Hermitian so that the formalism admits a natural extension to non-Hermitian initial H(E)s.
Cite
@article{arxiv.quant-ph/0403223,
title = {Linear representation of energy-dependent Hamiltonians},
author = {Miloslav Znojil},
journal= {arXiv preprint arXiv:quant-ph/0403223},
year = {2007}
}
Comments
14 pages - first half of the material to be presented during 2nd International Workshop on Pseudo-Hermitian Hamiltonians in June (cf. http://www.ujf.cas.cz/PTsymmetry)