New method for solving multidimensional scattering problem
The quantum mechanical problem of scattering of a particle with internal structure is studied. A new method is proposed without expanding the wave function over some basis and without calculating matrix elements of the Hamiltonian. For some variables \(\Omega\) characterizing the scatterer a difference net \(\Omega_ i\) is introduced, the distance between the nodes is characterized by the integration step h. These variables are discrete. One variable R (the distance from the particle to the center of mass of the scatterer) is continuous. The multidimensional Schrödinger equation is approximated by a system of differential-difference equations for the vector \(\psi\) (R,\(\Omega\)). The scattering problem is formulated by the procedure of the author [J. Comput. Phys. 65, 1-17 (1986; Zbl 0588.65064)] as a system of nonlinear functional equations the solution of which is equivalent to the determination of the wave function. As an example the ground state energies of the hydrogen atom in a homogeneous magnetic field are calculated. Scattering of a neutral particle on a di-atomic molecule is mentioned as another example.
scientific article; zbMATH DE number 4176399