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Widagda, I Gusti Agung
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SOLUTION OF THE TIME-INDEPENDENT SCHRÖDINGER EQUATION FOR THE ROSEN–MORSE POTENTIAL BY USING THE GALERKIN METHOD Widagda, I Gusti Agung; Artawan, Nengah; Trisnawati, Ni Luh Putu; Adnyana, I Gusti Agung Putra; Paramarta, Ida Bagus Alit
Indonesian Physical Review Vol. 8 No. 3 (2025)
Publisher : Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/ipr.v8i3.492

Abstract

This study presents a numerical solution to the time-independent Schrödinger equation (TISE) for the Rosen-Morse potential using the Galerkin method. The Rosen-Morse potential, commonly used in atomic and molecular physics, has known analytical solutions under certain conditions. By transforming the TISE into a Jacobi differential equation, the analytical wave function and energy levels can be derived. However, analytical solutions are limited to ideal cases, highlighting the need for numerical methods in more general scenarios. The Galerkin method is implemented by expanding the wave function using Sine basis functions and projecting the TISE onto this basis. The resulting eigenvalue problem is solved by constructing the Hamiltonian matrix from kinetic and potential energy operators. Numerical results from the Galerkin method are compared with analytical solutions using graphical analysis, percentage error (% error), and statistical tests, including the Mann-Whitney U test. The results demonstrate that the probability densities obtained using the Galerkin method closely approximate the analytical solution. This is visually evident from the overlapping of probability density plots from both methods. The percentage error of the probability densities is below 1 %, entirely.  Furthermore, the Mann–Whitney U test yields a p-value less than 0.05, indicating that the differences between the two sets of probability densities are statistically insignificant at the 95% confidence level. These findings highlight the Galerkin method’s effectiveness and accuracy as a robust numerical tool for solving the TISE with the Rosen-Morse potential.  
Analisis Spasial Penentuan Tipe Iklim Menurut Klasifikasi Schmidt-Ferguson Menggunakan Metode Thiessen-Polygon Di Kabupaten Bojonegoro Berdasarkan Data Curah Hujan Tahun 2016–2022 Hidayat, Alyi Savitri Astriyani; Baskoro, Winardi Tjahyo; Unsuriyah, Zumrotul; Yuliara, I Made; Widagda, I Gusti Agung; Pramarta, Ida Bagus Alit; Kurnia, Wenas Ganda
Kappa Journal Vol 7 No 3 (2023): Desember
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/kpj.v7i3.23128

Abstract

Research on Schmidt-Ferguson climate classification and Thiessen polygon mapping in Bojonegoro Regency, East Java has been carried out based on rainfall data during the 2016–2022 period. The aim of this research is to determine climate types according to the Schmidt-Ferguson classification and the spatial distribution of climate types using the Thiessen Polygon method in Bojonegoro Regency, East Java. This process begins with collecting rainfall data, coordinates and height of rain posts. From the analysis results obtained, Bojonegoro Regency has 4 types of climate based on the Schmidt-Ferguson classification, namely: Very Wet (A), Wet (B), Slightly Wet (C) and Dry (F). While based on Thiessen Polygon mapping, type A distribution has an area of 323.02 km2, climate type B classification covering an area of 962.22 km2, Classification of climate type C covering an area of 669.95 km2 and climate type F classification covering an area of 374.07 km2.   
Co-Authors Adnyana, I Gusti Agung Putra Artawan, Nengah Hidayat, Alyi Savitri Astriyani Ida Bagus Alit Paramarta KURNIA, WENAS GANDA Pramarta, Ida Bagus Alit Tjahyo Baskoro, Winardi Trisnawati, Ni Luh Putu Unsuriyah, Zumrotul Yuliara, I Made