Recovery of the matrix potential of the one-dimensional Dirac equation from spectral data
Abstract
Abstract A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand–Levitan equation and the Fourier–Legendre series expansion of the transmutation kernel. A linear algebraic system of equations is obtained, which can be solved numerically. To the best of our knowledge, this is the first practical method for the solution of the inverse problem for the one-dimensional Dirac equation on a finite interval.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Numerical methods in inverse problems
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- Inverse Problems
- Volume
- 42
- Issue
- 1
- Pages
- 015006–015006
- Publication date
- 6 January 2026
- Language
- EN