A Practical Method for Solving the Inverse Quantum Scattering Problem on a Half Line

Abstract

Abstract A method for solving inverse quantum scattering problems on a half line is proposed. It is based on the application of the transmutation operators and recent results on series expansion of the integral transmutation kernels. From the corresponding Gel’fand-Levitan equation a system of linear algebraic equations is derived for the coefficients of the Fourier-Legendre series expansion of the output (transmutation operator) kernel. It is shown that the knowledge of the very first coefficient is sufficient for recovering the potential and hence for solving the inverse problem. A numerical illustration is presented.