High-Order B-Spline Finite Difference Approach for Schrodinger Equation in Quantum Mechanics

This paper presents a new numerical method for solving the quantum mechanical complex-valued Schrodinger equation (CSE). The technique combines a second-order Crank-Nicolson scheme based on the finite element method (FEM) for temporal discretisation with nonic B-spline functions for spatial discretisation. This method is unconditionally stable with the help of Von-Neumann stability analysis. To verify our methodology, we examined an experiment utilising a range of error norms to compare experimental outcomes with analytical solutions. Our investigation verifies that the suggested approach works better than current methods, providing better accuracy and efficiency in quantum mechanical error analysis.