Geometric Spectral Inversion

2012/06/19 by Richard L. Hall, Hall, Richard L.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1206.4288

20 pages, 7 figures; 13th Regional Conference on Mathematical Physics, October 27 - 31, 2010, Antalya, Turkey

arxiv created 2012/06/19 · arxiv updated 2012/06/20

Abstract

A discrete eigenvalue E_n of a Schroedinger operator H = -Δ+ vf(r) is given, as a function F_n(v) of the coupling parameter v≥ v_c. It is shown how the potential shape f(x) can be reconstructed from F_n(v). A constructive inversion algorithm and a functional inversion sequence are both discussed.

Related

• Inverse problems, trace formulae for discrete Schrödinger operators
• A semi-classical inverse problem II: reconstruction of the potential
• Sampling The Lowest Eigenfunction to Recover the Potential in a One-Dimensional Schrödinger Equation
• Property C for ODE and applications
• Inverse spectral problem for the Schrödinger operator on the square lattice