Linear representation of energy-dependent Hamiltonians
arXiv:quant-ph/0403223 · doi:10.1016/j.physleta.2004.04.036
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.
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)
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- Schroedinger equations with indefinite effective mass
- Theory of response to perturbations in non-Hermitian systems using five-Hilbert-space reformulation of unitary quantum mechanics
- Bound state solutions of the Klein Gordon equation with energy-dependent potentials