DISCAPESM                Library "JINRLIB"                       

    Authors: T.P.Puzynina, Vo Trong Thach                            You are
    Environment: Maple/Windows                                       
                                                                     visitor here.

              On Numerical Solution of Direct and Inverse Scattering
       Problems for Spherically Symmetric Potentials Depending on Parameters

    The scattering problem for the radial Schrödinger equation, in contrast to 
    a statement of Cauchy's problem, is formulated as a boundary value problem for 
    a wave function with a non-linear asymptotic condition with exclusion of an unknown 
    phase shift. The phase shift is determined after calculation of the wave function 
    by taking into account its asymptotic behavior and applying the iteration schemes 
    of a continuous analog of Newton's method (CANM).
    The inverse problem for an equation with a potential depending on the parameters is
    reduced to minimization problem with respect to the parameters for the functional 
    that describes the sum of squares of deviations of the specified values of phase 
    shifts from the corresponding calculated values.
    Basic features of the computational schemes are demonstrated by solution of the 
    problem with Morse's potential which admits analytical solution and also by solving 
    the problem with Woods-Saxon's potential.
    
    A guide (in Russian) to the use of the software complex DISCAPESM see DISCAPESM_Guide.

    Examples of using for solving direct and inverse scattering problems on different 
    potentials:
       Morse's potential:
          DISCAPESM_PMORSE1.mw
          DISCAPESM_PMORSE2.mw
       Woods-Saxon's potential
          DISCAPESM_PWS.mw

    References:
    1. Т.П.Пузынина, Во Чонг Тхак. О численном решении прямой и обратной задачи рассеяния
       на сферически симметричных потенциалах, зависящих от параметров // Вестник РУДН. 
       Серия «Математика. Информатика. Физика». 2012, №4, С.73–86. 
       (DISCAPESM_Article.pdf, in Russian)