Algorithm for Computing Wave Functions, Reflection and Transmission Matrices of the Multichannel Scattering Problem in the Adiabatic Representation using the Finite Element Method

In adiabatic representation the multichannel scattering problem for a multidimensional Schro¨dinger equation is reduced to the boundary value problem (BVP) for a system of coupled self-adjoined second-order ordinary differential equations on a finite interval with homogeneous boundary conditions of the third type at the left and right boundary points in the framework of the Kantorovich method using adiabatic basis of surface functions depending on longitudinal variable as a parameter. The homogeneous third-type boundary conditions for the desirable wave functions of the BVP are formulated using the known set of linear independent regular and irregular asymptotic solutions in the open channels of the reduced multichannel scattering problem on an axis which involve the desirable reflection and transmission amplitude matrices, and the set of linear independent regular asymptotic solutions in the closed channels.

• Gusev A.A.

• Прикладные науки. Медицина. Технология

• Социальные (общественные) науки
• Науки о человеке