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The inverse quantum scattering problem for the perturbed Bessel equation isconsidered. A direct and practical method for solving the problem is proposed.It allows one to reduce the inverse problem to a system of linear algebraicequations, and the potential is recovered from the first component of thesolution vector of the system. The approach is based on a special formFourier-Jacobi series representation for the transmutation operator kernel andthe Gelfand-Levitan equation which serves for obtaining the system of linearalgebraic equations. The convergence and stability of the method are proved aswell as the existence and uniqueness of the solution of the truncated system.Numerical realization of the method is discussed. Results of numerical testsare provided revealing a remarkable accuracy and stability of the method.

A transmutation operator method for solving the inverse quantum scattering problem