Calculation of He atomic energy levels using the first order perturbation theory taught in the Basic Quantum Mechanics course has led to relatively large errors. To improve its accuracy, several methods have been developed but most of them are too complicated to be understood by undergraduate students. The purposes of this study are to apply a simple matrix method in calculating some of the lowest energy levels of He atom (1s2, triplet 1s2s, and singlet 1s2s states) and to reduce errors obtained from calculations using the standard perturbation theory. The convergence of solutions as a function of the number of bases is also examined. The calculation is done analytically for 3 bases and computationally with the number of bases using MATHEMATICA. First, the 2-electron wave function of the Helium atom is written as the multiplication of two He+ ion wave functions, which are then expanded into finite dimension bases. These bases are used to calculate the elements of the Hamiltonian matrix, which are then substituted back to the energy eigenvalue equation to determine the energy values of the system. Based on the calculation results, the error obtained for the He ground state energy using 3 bases is 2.51 %, smaller than the errors of the standard perturbation theory (5.28 %). Despite the fact that the error is still relatively large from the analytical calculations for singlet-triplet 1s2s energy splitting of He atom, this error is successfully reduced significantly as more bases were used in the numerical calculations. In particular, for n = 25, the current calculation error for all states is much smaller than the errors obtained from calculations using standard perturbation theory. In conclusion, the analytical calculations for the energy eigenvalue equation for the 3 lowest states of the Helium atom using 3 bases have been carried out. It was also found in this study that increasing the number of bases in our numerical calculations has significantly reduced the errors obtained from the analytical calculations.

This study reports for the first time the theoretical prediction of structural, electronic, elastic and optical properties of cubic BaLiCl3, BaLiBr3, and BaLiI3 perovskites. The corresponding properties of the well-known BaLiF3 are also theoretically investigated. Density Functional Theory (DFT) using the Generalized Gradient Approximation (GGA) was implemented within the Quantum Espresso package to investigate the properties of the perovskites. The results revealed that BaLiX3 (X = F, Cl, Br, and I) are in ionic crystal forms with optimized lattice parameters of 4.04, 4.90, 5.21, and 5.66 Å, respectively. The minor band gaps were found to be 6.62 eV (Γ→Γ), 4.29 eV (R→Γ), 3.50 eV (R→Γ), and 2.58 eV (R→Γ) for the respective compounds. The investigation of their elastic properties indicated that these perovskites are all mechanically stable, while only BaLiBr3 and BaLiI3 are malleable. Finally, the studied perovskites exhibit excellent optical properties, including low reflectivity and high absorption in the ultraviolet region. Hence, it is predicted that these perovskites are suitable for various optoelectronic applications involving absorption in the UV region. However, BaLiBr3 and BaLiI3 are more favorable than BaLiF3 and BaLiCl3 to be deposited as thin films due to their flexibility.

Abstrak Penelitian ini bertujuan untuk mengidentifikasi pola distribusi perubahan stress coulomb yang dapat digunakan untuk melihat gempabumi susulan yang terjadi dalam jarak dan dalam rentang waktu yang dekat. Penelitian ini menggunakan data gempabumi yang terjadi pada 2 agustus 2019 dengan Mw 6,9 di Tugu Hilir, Indonesia, pada koordinat 104,825 BT dan 7,267 LS dengan kedalaman 52,8 km (USGS) memiliki mekanisme fokus (Strike, dip, rake) adalah (201°, 49°, 54°). Data ini kemudian diolah dengan menggunkan software coulomb 3.3 pada matlab. Dari hasil penelitian didapatkan bahwa gempabumi ini gempabumi ini memiliki peningkatan stress coulomb (≤ 1,0 bar) berarah timurlaut-baratdaya dan merupakan daerah gempabumi susulan terjadi. Sedangkan daerah penurunan stress coulomb (≤ -1,0 bar) berarah barat-laut tenggara. Kata kunci: gempabumi, perubahan stress coulomb, coulomb3.3, USGS, Tugu Hilir. Abstract This research aims to Identifed the distribution coulomb stress changed that can be used to seesthe subsequent earthquake that occurs within a short distanceand time span. This research uses earthquake data on 2 August 2019 with Mw 6.9 in Tugu Hilir, Indonesia, at 104.825°E and 7.267°S, with 52.8 km depth (USGS). The focus mechanism (strike, dip, rake) is (201°, 49°, 54°). This data prosessed by using Coulomb 3.3 software in MATLAB. The result found that this main earthquake had an increase coulomb stress changed (≤ 1.0 bar) in the northeast-southwest and was a subsequent earthquake area. Whereas the area of decrese of coulomb stress changed (≤ -1.0 bar) in the northwest-southeast.  Keywords: earthquake, coulomb stress changed, coulomb 3.3, USGS, Tugu Hilir

ABSTRAK Penelitian menggunakan metode HVSR (Horizontal to Vertical Spectral Ratio) telah dilakukan untuk memetakan daerah yang rawan terhadap gempa bumi di Desa Bitobe. Tujuan dari penelitian ini adalah mengetahui nilai periode dominan tanah dan percepatan tanah maksimum, serta untuk membuat peta PGA dan juga peta Mikrozonasi. Pengambilan data dilakukan pada 45 titik dengan jarak antar titik ± 250 m dari titik satu ke titik lainnya dengan waktu perekaman selama ± 20 menit menggunakan TDS tipe 303S. Data yang diperoleh diolah menggunakan software Datapro, Geopsy, Surfer 13, dan Google Earth. Hasil pengolahan data diperoleh nilai frekuensi dominan (). Parameter ini digunakan untuk meghitung nilai PGA menggunakan persamaan empiris Kanai dengan data katalog gempa bumi dari tahun 1966-2016. Metode Mc.Guirre dan Esteva hanya menggunakan data katalog gempa saja dalam menghitung PGA. Berdasarkan hasil penelitian, didapatkan bahwa nilai frekuensi dominan berkisar antara 0,273 Hz – 17,887 Hz. Nilai percepatan tanah maksimum berdasarkan persamaan empiris Kanai berkisar antara 32,319 gal – 261,178 gal, Mc.Guirre berkisar antara 128,215 gal – 134,862 gal dan Esteva berkisar antara 147,359 gal – 156,007 gal. Hasil dari ketiga persamaan ini memiliki perbedaan dengan peta hazard gempa Indonesia. Kata kunci: HVSR, Mikrozonasi, Kanai, Mc.Guirre, Esteva, Bitobe ABSTRACT The research using HVSR (Horizontal to Vertical Spectral Ratio) has been carried out to map the disturb areas to earthquakes in Bitobe village. The aims of this research are to determine the values of soil dominant frequency and the peak ground acceleration than make PGA map and also microzonation map. Data were collected at 45 points with the distance between points ± 250 meters from one point to the other with ± 20 minutes of recording time used TDS 303S type. The data were processed using software Datapro, Geopsy, Surfer 13, and Google Earth. The result of data processing was dominant frequency value (). This parameter was used to calculate the peak ground acceleration with Kanai empirical equations. The earthquakes catalog data were used from 1966-2016. Mc.Guirre and Esteva method only used the earthquakes catalog data to calculated the PGA. According to this research, it was obtained that the values of the dominant frequency was about 0,273 Hz – 17,887 Hz. The values of peak ground acceleration based on Kanai empirical equations about 32,319 gal – 261,178 gal, Mc.Guirre about 128,215 gal – 134,862 gal and Esteva about 147,359 gal – 156,007 gal. The result of this third equations have different with the earthquakes hazard map of Indonesia. Key Words: HVSR, Microzonation, Kanai, Mc.Guirre, Esteva, Bitobe

Abstrak Telah dilakukan analisis pola dan distribusi hujan berdasarkan ketinggian tempat di pulau Flores. Data rata-rata bulanan untuk mendapatkan pola curah hujan, data curah hujan harian ke dasarian untuk mendapatkan data curah hujan dan data periode curah hujan selama musim hujan. Penelitian ini menggunakan software Geographic Information System (GIS) untuk membuat peta distribusi curah hujan dan di analisis menggunakan metode Rancangan Acak Lengkap (RAL) untuk mendeteksi perbedaan nilai tengah variabel pengamatan pada elevasi yang berbeda. Berdasarkan grafik pola hujan yang ada di pulau Flores adalah pola hujan monsunal. Hasil dari perhitungan menggunakan RAL, diperoleh nilai populasi pengamatan P1 pada ketinggian tempat (0-300 m dpl) dengan curah hujan rata-rata 851,75 mm dan periode musim hujan rata-rata 10,50 dasarian. P2 pada ketinggian tempat (301-600 m dpl) memiliki curah hujan rata-rata 1367,75 mm dan periode musimhujan rata-rata 13,75 dasarian. P3 pada ketinggian tempat (601-900 m dpl) memiliki curah hujan rata-rata 1875,25 mm dan periode musim hujan rata-rata 15,75 dasarian. P4 pada ketinggian tempat (901-1200 m dpl) memiliki curah hujan rata-rata 3164,50 mm dan periode musim hujan rata-rata 22,25 dasarian. Hal ini menunjukan ketinggian tempat memiliki pengaruh terhadap curah hujan dan periode musim hujan di pulau Flores.Kata Kunci: Pola hujan; curah hujan; periode musim hujan; Geographic Information System (GIS); Rancangan Acak Lengkap (RAL). Abstract An analysis of rainfall patterns and distribution based on altitude on the island of Flores has been done. Monthly average data to get rainfall patterns, daily to basic rainfall data to get rainfall data, and rainfall period data during the rainy season. This study used Geographic Information System (GIS) software to create rainfall distribution maps and is analyzed using the Completely Randomized Design (CRD) method to detect differences in mean values of observational variables at different elevations. Based on a chart of rain patterns on Flores island is a monsoonal rain pattern. The results of calculations using RAL, observational population obtained values P1 at altitude (0-300 m asl) with an average rainfall of 851.75 mm and an average rainy season period of 10.50 dasarian. P2 at altitude (301-600 m asl) has an average rainfall of 1367.75 mm and an average rainy season period of 13.75 dasarian. P3 at altitude (601-900 m above sea level) has an average rainfall of 1875.25 mm and an average rainy season period of 15.75 dasarian. P4 at altitude (901-1200 m asl) has an average rainfall of 3164.50 mm and an average rainy season period of 22.25 dasarian. This shows that altitude has an influence on rainfall and the rainy season period on Flores Island. Keywords: Rain patterns; rainfall, periods of the rainy season; Geographic Information System (GIS); Completely Randomized Design (CRD).