Numerical solution of Schrödinger equation using matrix method
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Abstract
This study presents a numerical method for solving the matrix Schrödinger equation using symmetric tridiagonal and heptadiagonal matrices. The approach is based on the n-th order Taylor series expansion to approximate second-order derivatives. It is applied to compute bound and scattering states for a one-body problem in one-dimensional motion with a square well potential, using natural units. Comparison with analytical solutions indicates that the symmetric heptadiagonal matrix offers improved accuracy, particularly in calculating phase shifts for scattering states.