Application of cubic splines for solving schrodinger equation for study of sctructure of atomic nuclei

Bazhin A.S.

“Dubna” University, e-mail

Cubic spline interpolation is applied for solving Schrodinger equation [1]. The problem is reduced to eigenvalue and eigenvectors problem of matrix. The application of spline interpolation allows to find picewise smooth solutions, using a not very small grid step and size of matrix. The method is applied for solving radial Schrodinger equation in shell model of spherical nuclei and for solving hyperradial equations. Wave function and energy of ground state of 9Be nucleus were calculated in alpha-cluster model (α + α + n) using spherical harmonic decomposition [2]. The method was written on C++ language using parallel programming libraries (OpenMP, NVIDIA CUDA). The charge distribution for the 9Be nucleus was calculated and agreement with the experimental distribution (e.g., [3]) was obtained.


1. Марчук G.I. Methods of computational mathematics. ‒ M.: Nauka, 1980.

2. R.I. Dzhibuty, K.V. Shitikovа, Hyperspherical functions method in the atomic and nuclear physics. ‒ М.: Energoatomizdat, 1993 (in Russian).

3. V.I. Zagrebaev, A.S. Denikin, A.V. Karpov, A.P. Alekseev, M.A. Naumenko, V.A. Rachkov, V.V. Samarin, V.V. Saiko, NRV Web Knowledge Base on Low-Energy Nuclear Physics,


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