Energy-dependent Hamiltonians and their pseudo-Hermitian interpretation

Miloslav Znojil; Hynek Bila; Vit Jakubsky

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arXiv · quant-ph/0312148

Energy-dependent Hamiltonians and their pseudo-Hermitian interpretation

Miloslav Znojil·Hynek Bila·Vit Jakubsky

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Abstract

The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary non-Hermitian operator K which remains energy-independent. Practical merits of such an approach to the Schroedinger equations with energy-dependent potentials are illustrated using their quasi-exactly solvable example.

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Miloslav Znojil, Hynek Bila, Vit Jakubsky. 2003-12-17. Energy-dependent Hamiltonians and their pseudo-Hermitian interpretation. https://arxiv.org/abs/quant-ph/0312148

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