Inverse Feshbach's problem: Solvability and solutions

• URL: http://arxiv.org/abs/2608.18600v1
• Date: Wed, 19 Aug 2026 06:42:13 GMT
• Title: Inverse Feshbach's problem: Solvability and solutions
• Abstract summary: Given a certain specific, $M$ by $M$ matrix form of the Feshbach's effective (i.e., energy-dependent) Hamiltonian $H(M)_e!f!f!f!f!f(E)$, the inverse-problem reconstruction of the full-space is considered.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given a certain specific, $M$ by $M$ matrix form of the Feshbach's effective (i.e., energy-dependent) Hamiltonian $H^{(M)}_{e\!f\!f}(E)$, the inverse-problem reconstruction of the full-space, $N$ by $N$ matrix Hamiltonian $H^{(N)}$ is considered and reduced to the solution of a coupled set of polynomial algebraic equations. Using computer-assisted symbolic manipulations, an explicit algebraic reconstruction of $H^{(N)}$ is found feasible at not too large $K = N-M$.

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