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The ABX3 perovskite materials have recently emerged as one of the most promising materials for optoelectronic applications. In the present study, novel perovskites in the form of InZnCl3 and InCdCl3 are computationally investigated to determine their key characteristics, including structural, mechanical, electronic, and optical characteristics. These characteristics were evaluated using the density functional theory (DFT) implemented in the quantum espresso code. The results indicated that both materials exhibit chemical, dynamic, and mechanical stability. Moreover, these perovskites are predicted to be ductile, rendering them suitable for a broad array of optoelectronic applications, including solar cells. The electronic band structure and the density of states of the materials revealed their characteristics as indirect semiconductors with band gap energy values of 0.96 eV for InZnCl3 and 1.83 eV for InCdCl3 perovskites. The optical properties calculations also unveiled that these perovskites possess strong absorption in the visible-ultraviolet spectrum (up to 106 cm−1) and low reflectivity. The calculated refractive index and extinction coefficient of the compounds were also predicted in this study. These collective findings strongly suggest the potential applications of these novel materials in optoelectronic devices.

This study discusses the feasibility of diversifying the scope of application of lead-free Sr3ZBr3 (Z = As, Sb) as promising materials for their enhanced electronic, mechanical, optical, thermodynamic, and thermoelectric properties using first-principles calculation based on Density Functional Theory (DFT). Both compounds have cubic crystal structures, and both materials' dynamic stability is validated by the lack of negative frequencies in their phonon dispersion spectra. Besides ground state physical characteristics, we also examined the impact of hydrostatic pressure (0–21 GPa) on electronic, mechanical, and optical properties. The lattice parameters exhibit a linear decrease from 6.27 to 5.61 Å for Sr3AsBr3 and 6.45 to 5.71 Å for Sr3SbBr3 under increasing pressure, attributed to bond length reduction, which alters their physical properties. Initially observed direct band gap (Γ-Γ) of Sr3AsBr3 and Sr3SbBr3 were 2.35 and 2.30 eV using modified Becke-Johnson (mBJ) functional which reduces to 1.15 and 0.82 eV as the compounds go from 0 to 21 GPa pressure. This study reveals enhanced optical properties under pressure, with broader spectral response, increased sensitivity, and improved dielectric constant. Optical absorption and conductivity also shift toward lower-energy photons. The investigation further shows that the compounds show brittle to ductile transition under high pressure. Their ductility and anisotropy nature are further enhanced with pressure along with other mechanical features. The thermodynamic properties indicate their ability to withstand and perform well at high temperatures and pressures. Lastly, the thermoelectric properties of Sr3ZBr3 (Z = As, Sb) were assessed through electrical and thermal conductivity, Seebeck coefficient, power factor (PF), and figure of merit (ZT) as a function of temperature. Both compounds exhibit high PF and near-unity ZT. These findings underscore their potential as strong candidates for optoelectronic and thermoelectric devices, owing to their direct bandgap and exceptional properties.

This study aims to investigate the structural, mechanical, optical, electronic, and thermoelectric properties of novel double perovskites Tl2GeCl6 and Tl2GeBr6. The Quantum Espresso code was employed to perform the Density Functional Theory (DFT) calculation on the perovskites’ characteristics. The results indicated that both materials exhibit chemical and structural stability, with equilibrium lattice constants of 10.08 Å and 10.55 Å for Tl2GeCl6 and Tl2GeBr6, respectively. The calculated elastic parameters and elastic moduli data also demonstrated that the new double perovskites exhibit mechanical stability while the calculated electronic band structure and the density of states using the PBE functional indicated that the materials are semiconductors with energy gap values of 0.3 eV for Tl2GeBr6 and 1.72 eV for Tl2GeCl6, respectively. Using more accurate SCAN approximation, the energy gaps were refined to 0.53 eV for Tl2GeBr6 and 2.10 eV for Tl2GeCl6. Additionally, the calculated dielectric functions, extinction coefficient and absorption coefficients of Tl2GeCl6 and Tl2GeBr6 strongly suggest the exceptional optical response of these materials. Notably, Tl2GeBr6 is estimated to have a particularly strong visible-light absorption capacity, positioning it as a promising absorber for perovskite solar cells. These findings are also supported by the low reflectivity values observed. Finally, the analysis of their thermoelectric properties revealed the excellent thermoelectric properties of Tl2GeCl6 and Tl2GeBr6, as indicated by their high figures of merit, predicted to be 0.73 and 0.68 for the respective perovskites.

Here, first-principles calculations have been employed to make a comparative study on structural, mechanical, electronic, and optical properties of new Ca3MF3 (M = As and Sb) photovoltaic compounds under pressure. The findings disclose that these two systems possess a direct band gap, showcasing a large tunable range under pressure, effectively encompassing the visible light spectrum. Adjusting various levels of hydrostatic pressure has effectively tuned both the band alignment and the effective masses of electrons and holes. Both compounds were initially identified as brittle materials at 0 GPa pressure; however, as the pressure increases, they transform, becoming highly anisotropic and ductile. Due to the material's mechanical robustness and enhanced ductility, as evidenced by its stress-induced mechanical properties, the Ca3MF3 (M = As and Sb) material shows potential for use in solar energy applications. Furthermore, as the influence of external pressure increases, the absorption edge seems to move slightly towards lower energy region. Optical properties show that the materials studied might be used from several optoelectronic devices in the visible and ultraviolet range area. Our findings show that pressure considerably influences the physicochemical properties of Ca3MF3 (M = As and Sb) compounds, which is a promising feature that can be useful for optoelectronic and photonic applications, for instance, light-emitting diodes, photodetectors, and solar cells.

The approximate solution to the Schrödinger equation of exotic doubly muonic helium-like systems has been obtained using a simple matrix method based on hydrogenic s-states. Each system considered consists of a positively charged nucleus surrounded by 2 negatively charged muons XZ+μ-μ- (2 Z 36). The present work aims to obtain approximate ground-state energies of the systems and to decompose the energies in terms of the basis states used. Here, the wave function was expressed as a linear combination of 15 eigenfunctions, each written as the product of two hydrogenic s-states. The elements of the Hamiltonian matrix were calculated and finally, the energy eigenvalue equation was numerically solved to obtain the ground-state energies of the systems with their corresponding eigenvectors. From the results, ground-state energies of all systems were in agreement with others from the literature, with percentage differences between 0.03% and 2.05%. The analysis of the probability amplitudes from the eigenvectors showed that the 1s1s state made the largest contribution to the ground state energies of the systems, approaching 90.99%, 96.98% and 98.54% for He2+μ-μ- , Li3+μ-μ- , and Be4+μ-μ- , respectively. Keywords: Doubly muonic helium-like systems, ground state energy, hydrogenic basis states, matrix mechanics, Schrödinger equation

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.

This study aims at implementing a truncated matrix approach based on harmonic oscillator eigenfunctions to calculate energy eigenvalues of anharmonic oscillators containing quadratic, quartic, sextic, octic, and decic anharmonicities. The accuracy of the matrix method is also tested. Using this method, the wave functions of the anharmonic oscillators were written as a linear combination of some finite number of harmonic oscillator basis states. Results showed that calculation with 100 basis states generated accurate energies of oscillators with relatively small coupling constants, with computation time less than 1 minute. Including more basis states could result in more correct digits. For instance, using 300 harmonic oscillator basis states in a simple Mathematica code in about 8 minutes, highly accurate energies of the oscillators were obtained for relatively small coupling constants, with up to 15 correct digits. Reasonable accuracy was also found for much larger coupling constants with at least three correct digits for some low lying energies of the oscillators reported in this study. Some of our results contained more correct digits than other results reported in the literature.

A preliminary study has been carried out on the radial properties of the hydrogenic systems using the Laguerre polynomial. The aims of this study were to investigate radial properties of hydrogenic ions by evaluating the radial probability density, the most probable radial distance and the average distance of electron from the nuclei of hydrogenic ions. Based on the research results for Z=1 to Z=10 with the principal quantum number (n)=1 to 5, 150 radial function forms, 150 radial probability density, 150 most probable radial distance values and 150 electron average distance values were obtained. The most probable radial distance from the nucleus was compared with the Bohr model and showed the same results as the Bohr model.

This study aims to use hydrogenic orbitals within an analytic and numeric parameter-free truncated-matrix method to solve the projected Schrödinger equation of some Helium-like ions (3 ≤ Z ≤ 10). We also derived a new analytical expression of the ion ground state energies, which was simple and accurate and improved the accuracy of the analytic calculation, numerically using Mathematica. The standard matrix method was applied, where the wave function of the ions was expanded in a finite number of eigenvectors comprising hydrogenic orbitals. The Hamiltonian of the systems was calculated using the wave function and diagonalized to obtain their ground state energies. The results showed that a simple analytic expression of the ground state energies of He-like ions was successfully derived. Although the analytic expression was derived without involving any variational parameter, it was reasonably accurate with a 0.12% error for Ne8+ ion. From this method, the accuracy of the analytic energies was also numerically improved to 0.10% error for Ne8+ ion. The results clearly showed that the energies obtained using this method were more accurate than the hydrogenic perturbation theory and the uncertainty principle-variational approach. In addition, for Z > 4, our results were more accurate than those from the geometrical model.

This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.

Pendekatan Born-Oppenheimer diterapkan untuk menghitung tingkat energi vibrasi keadaan dasar molekul hidrogen. Persamaan Schrodinger untuk inti atom diselesaikan dengan menggunakan metode semi-klasik, di mana inti atom diasumsikan bergerak secara klasik dalam sumur potensial dan energi vibrasi ditentukan dengan menerapkan aturan kuantisasi kuantum. Potensial yang digunakan pada penelitian adalah potensial Morse. Dalam penelitian ini, tingkat energi vibrasi dihitung dengan metode numerik, yaitu metode integrasi Simpson dan metode regula falsi. 15 Tingkat energi vibrasi dari molekul H2 diperoleh dan dibandingkan dengan data hasil eksperimen. Perbandingan ini mengindikasikan pendekatan yang digunakan pada penelitian ini memberikan hasil yang sangat akurat pada tingkat energi vibrasi yang relatif rendah (0≤n≤4), dengan kesalahan kurang dari 0,7%, dan untuk 5≤n≤8 dengan kesalahan maksimum 7,3%. Keakuratan menurun ketika tingkat energi vibrasi meningkat. Secara khusus, untuk n = 13 dan n = 14, kesalahan meningkat secara signifikan, menunjukkan gagalnya pendekatan ini untuk tingkat energi vibrasi yang relatif tinggi, khususnya untuk dua tingkat energi ini. Born-Oppenheimer approximation was applied to calculate vibrational energy levels of ground state of Hydrogen molecule. The Schrodinger equation for the nuclei was solved using a semi-classical method, in which the nuclei are assumed to move classically in a potential well and the vibrational energies are determined by applying the quantum mechanical quantization rules. Potential used in this research was the Morse potential. Here, vibrational energy levels of the molecule were calculated using numerical methods, i.e. Simpson integration method and false position method. 15 Vibrational energy levels of the H2 molecule were obtained and compared to the corresponding results from experiments. The comparison indicated that the approximation used in this research yielded very accurate results for relatively low vibrational levels (0≤n≤4), with errors being less than 0.7% and for 5≤n≤8 with maximum of 7.3% errors. The accuracy decreased as the vibrational levels increased, as expected. In particular, for n=13 and n=14, errors significantly increased, indicating the breakdown of the approximation for relatively high vibrational levels, in particular for these two energy levels.

This study aims to explore for the first time the mechanical, electronic, optical and thermoelectric properties of cubic lead-free perovskites InSnBr _3 and InSnI _3 to investigate their potential applications in solar cell devices. Additionally, the previously examined InSnCl _3 perovskite is also included. The properties of the perovskites were determined using first-principles calculation based on the well-known Density Functional Theory (DFT) with the Generalized Gradient Approximation (GGA) functional implemented in the Quantum Espresso package. One of the most important findings was that the bandgaps of the compounds decrease and undergo an indirect-to-direct bandgap transition when Cl is replaced by Br and I. This indicates that InSnBr _3 and InSnI _3 perovskites are more suitable for solar cell applications. The bandgap energies for InSnCl _3 , InSnBr _3 , and InSnI _3 perovskites are 0.59 eV (R→X), 0.44 eV (R→R), and 0.24 eV (R→R), respectively. The improved band gaps using the HSE06 functional are 2.35 eV, 2.13 eV, and 2.01 eV for the respective perovskites. The materials were found to possess chemical, mechanical, and thermodynamic stability as well as ductile behaviour. Furthermore, the materials exhibit remarkable optical properties, including high absorption coefficients and relatively small reflectivity. The calculated thermoelectric properties indicated high electrical conductivity and reasonable figure of merit values, making them promising candidates for the application in thermoelectric devices.

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 aims at comprehensively evaluating and comparing the goodness-of-fit of several potential energy curves (PECs), which are Morse, Manning-Rosen, Rosen-Morse and Modified-Rosen-Morse oscillators, to the corresponding experimental Rydberg-Klein-Rees (RKR) or RKR-style data of diatomic molecules. In this work, we also determined vibrational energies of the diatomics based on Bohr-Sommerfeld quantization rule. The goodness-of-fit to RKR data of 34 electronic states of 17 diatomics and the accuracy of the calculated vibrational energies were compared for the four oscillators and reported simultaneously for the first time in this study. These results showed that some oscillators demonstrated better goodness-of-fit than the others. Overall, the (Modified)-Rosen-Morse oscillators generated more accurate vibrational levels for most molecules studied, while Manning-Rosen oscillator was generally better for molecules in their excited electronic states. Although all oscillators performed well for more classical molecules, the Morse oscillator was superior to the other three in describing the ground states of 12C16O and 28Si32S. Particularly, it reproduced all 38 observed experimental ground state vibrational levels of 12C16O with error below 0.79% and even accurately predicted four states unobserved experimentally.

Sound Level Meter (SLM) is a tool used to measure the noise level for a moment. For improved performance, hence required a measure of noise level capable of displaying result automatically on the computer so that simplify user to observe and measure the noise. In this study, the design system of data acquisition consists of a MAX4466 sound sensor, Arduino UNO microcontroller, and computer to display the measurement result. The measurement results are displayed in the form of data and graphs. The display of software designed using the Delphi 7.0. The process of taking data in the room with a sound intensity of 44.6 dB. The value is the measurement result using the SLM tool, while the measurement results using the sound sensor performed every second during an interval of 30 seconds obtained an average of 44.19 dB. It can be seen that between the two results shows a relatively small difference, so it can be concluded that the design of this system is running well. Keywords: Noise, SLM, Sound sensor, Arduino Uno