The UTC Graduate School is pleased to announce that Matthew Gage Plott will present Doctoral research titled, Using Bertlmann-Martin Inequalities in Moment Theory to Solve Inverse Quantum Problems on 02/27/2026 at 4:15 PM in Lupton Hall 393. Everyone is invited to attend.
Computational Science
Chair: Ayça Çetinkaya
Co-Chair: Chris Cox
Abstract:
Reconstructing a 1D potential V(r) from a few bound-state energies, I present a GPU-accelerated Laplace-moment pipeline. Even moments are from the generalized Bertlmann–Martin (GBM) inequalities; odd moments are interpolated. A Padé continuation of the Laplace image L(q) is inverted analytically, where stable, and numerically otherwise (de Hoog–Knight–Stokes). Robustness comes from pruning obstructive poles and applying small-ensemble Padé averaging before inversion. Benchmarks on Coulomb, harmonic-oscillator, Hulthén, Kratzer, and a hyperbolic molecular potential reach sub-percent L^2 errors and are compared against an LSQ baseline. I also demonstrate the use of excited-state levels within the GBM recurrence. I conclude with a discussion of extensions to radial 3D problems and results from a hybrid Laplace–ML variant where physics-informed priors further reduce spectral data requirements.