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Edo Anugrah
Sriwijaya University
Education Physics

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High-Accuracy Numerical Solution of the One-Dimensional Schrödinger Equation Using the Numerov–Shooting Method Sopia Sopia; Dea Amalia; Edo Anugrah; Hamdi Akhsan; Melly Ariska
Jurnal Pendidikan Fisika dan Teknologi (JPFT) Vol 12 No 1 (2026): January-June (In Press)
Publisher : Department of Physics Education, Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jpft.v12i1.10794

Abstract

The Time-Independent Schrödinger Equation (TISE) plays a crucial role in quantum mechanics for obtaining the eigenenergies and wave functions of a system. This research numerically solves the TISE for the one-dimensional infinite potential well model by applying the Numerov method combined with the shooting technique. The Numerov method was chosen because it has an order of accuracy of O, making it effective for solving second-order differential equations with a very small truncation error. Numerov is used to solve the second order differential equation with a high degree of accuracy, while the shooting technique is applied to determine the eigenenergies that satisfy the physical boundary conditions of the system. Wave function normalization is performed using the Simpson integral so that the total probability is. Numerical validation is carried out by comparing the computed eigenenergies to the analytical solution  in dimensionless units for  up to . The results show that the numerical energies have a relatif error in the range of order  to , indicating that the Numerov method is capable of producing very accurate and consistent solutions. Based on these findings, the Numerov method can be used effectively in solving quantum mechanics problems that do not have analytical solutions.
Co-Authors Dea Amalia Hamdi Akhsan Melly Ariska Sopia Sopia