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Linear representation of energy-dependent Hamiltonians

Miloslav Znojil
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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.

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Miloslav Znojil. 2004-04-20. Linear representation of energy-dependent Hamiltonians. https://doi.org/10.1016/j.physleta.2004.04.036

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