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arXiv · 2602.20112

Inverse Quantum Potential Reconstruction via Generalized Bertlmann-Martin Inequalities

M. Gage Plott·F. Ayça Çetinkaya·Rick Mukherjee
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Abstract

Reconstructing a radial (1D) quantum potential, V(r), from a few bound-state energies is a long-standing inverse problem because limited spectral data must constrain an entire potential. We present a Laplace-moment reconstruction pipeline that links the Bertlmann-Martin gap bound to generalized Bertlmann-Martin (GBM) even-moment ladders, continues the Laplace transform with Pade approximants, and inverts the transform to recover rho(r) and V(r). Odd moments are supplied by a physically consistent interpolation scheme. Benchmark settings and diagnostics for Coulomb, harmonic oscillator, Hulthen, Kratzer, and hyperbolic-well cases are stated so each approximation stage can be assessed under a common empirical basis. The conclusions are therefore limited to the reported benchmark settings rather than offered as universal method claims.

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M. Gage Plott, F. Ayça Çetinkaya, Rick Mukherjee. 2026-05-11. Inverse Quantum Potential Reconstruction via Generalized Bertlmann-Martin Inequalities. https://doi.org/10.1142/s0129055x26610015

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