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JURNAL PEMBELAJARAN FISIKA

PROBABILITAS PARTIKEL DALAM KOTAK TIGA DIMENSI PADA BILANGAN KUANTUM n≤5

Indah Kharismawati, Bambang Supriadi, Rif'ati Dina Handayani

Published Feb 13, 2021• 0 citations
OpenAlex

Abstract

The goals of this research were to determine the particle probability density in three-dimensional box not perturbation on interval 0 until L/4 in quantum number n≤5. Type of this research was pure literature review research. The research method of Simpson rule at Matlab program. The result of the research were the probability to find particle (electron) in three dimensions box had determined by width size box (the position of particle) in position (x, y, z) so founded probability density depend on quantum number (nx, ny, nz)

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Complete solutions of particle in three dimensional box with variations in main quantum number

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Abstract Particle in a box is one of the applications of the Schrodinger equation. Schrodinger equation gives wave function which is used to determine the probability and expectation value of particle in a box. It is also can explain the energy levels of the particle. This study aimed to determine the probability, expectation values, and energy levels of a particle in a three-dimensional box with variations in main quantum numbers in each coordinate axis. The magnitude of the wave function and energy levels are influenced by the main quantum number and the width of the box. The results show that variations in the main quantum number influence the probability of particle in the three-dimensional box except for the width of the box <?CDATA $\frac{L}{2}$?> L 2 and L the probability of particle showing the same value in all variations of the main quantum number. Variations in the main quantum number also influence the expectation value of particle in a three-dimensional box except for the width of the box L the expectation value shows the same value in all variations of the main quantum number. All variations of the main quantum number also influence the magnitude of the energy level of the particle.

Journal of Physics Conference Series•May 1, 2020•0 citations
The goals of this research were to determine the particle probability density in three-dimensional box not perturbation on interval 0 until L/4 in quantum number n≤5. Type of this research was pure literature review research. The research method of Simpson rule at Matlab program. The result of the research were the probability to find particle (electron) in three dimensions box had determined by width size box (the position of particle) in position (x, y, z) so founded probability density depend on quantum number (nx, ny, nz)
Hamiltonian a known system in many matters does not guarantee that the equation can be resolved, e.g. due to minor disturbances such as electric fields or magnetic fields that can lead to slight changes in energy and its particle functions, for such issues it should be used disorder theory (perturbation theory). The perturbation theory can determine how much the result of the presence of disruption to energy levels and Eigen's functions. The energy possessed by particles in addition to being influenced by quantum numbers (nx, ny and nz) and the size of the potential box are also influenced by interference in the form of magnetic energy produced due to the motion of particles (electrons) in the core intrinsic magnetic field (proton) which affects the energy value does not appear due to the value of this magnetic energy disorder is very small, while for interference that is an extrinsic magnetic energy has shown a 10 (Tesla). The wider the size of the box then the energy that the particles have is smaller so that the energy level and the particle energy spectrum in the potential box will appear continuous. It can be concluded that the particle energy level relies on the length of the potential box, the quantum number of particles, and also the interference that particles have.
Static potential boxes represent an area that is limited by an infinite potential wall, where there is no external potential in it. The solution of the Schrodinger equation gives a wave function that can explain the energy level and determine the probability of finding a particle at any point. The main focus of the research in this paperwas to solve the solution to the energy levels, probabilities, and expectation values of a particle in a three-dimensional box, where control limits are given for the potential box width, namely and L for each situation. In this research, the results showed that probability meetings depend on changes in box width and quantum number of particles, while particle energy levels depend on the length of the box and the quantum number of particles. Based on the relation between probabilities and expectation values, the most stable size of the box to find the particles in ground state to the fourth excitation state is at the width of and L .
This research aims to develop computational visualization of the wave function and probability distribution of particles in a one dimensional infinite potential well. The wave function is obtained analytically from the time-independent Schrödinger equation and then normalized to give it probabilistic meaning. Numerical simulations are carried out using Python with the NumPy library for computation and Matplotlib for visualization, allowing manipulation of parameters such as box length and quantum number. The visualization results confirm the basic concepts of quantum mechanics, namely quantized energy levels, sinusoidal wave function forms with a specific number of nodes, and probability distributions that have several peaks and are always positive. The simulation also shows the correspondence between wave-function nodes and zero-probability points, as well as the increasing complexity of oscillations and variations in probability distributions as the quantum number increases. These findings are consistent with theoretical predictions and show that the computational approach is effective in visualizing abstract concepts in quantum mechanics, thereby clarifying the relationship between mathematical formulation and its physical interpretation.
Atom Tritium merupakan salah satu isotop atom hidrogen yang hanya memiliki sebuah elektron sehingga penelitian ini bertujuan untuk menentukan probabilitas menemukan electron atom tritium ( ) dalam ruang momentum dengan bilangan kuantum utama n 3. Penelitian ini termasuk dalam penelitian non-eksperimen dengan metode studi literatur terkait mekanika kuantum. Untuk menentukan data probabilitas momentum elektron atom Tritium ( ) digunakan perhitungan secara numerik menggunakan program Matlab R2021a. Hasil yang diperoleh pada penelitian ini berupa nilai probabilitas momentum elektron atom Tritium ( ) yang akan memberikan gambaran mengenai keberadaan elektron dalam ruang momentum. Berdasarkan hasil penelitian dapat ditunjukkan bahwa dalam ruang momentum, probabilitas ditemukannya elektron atom Tritium semakin meningkat seiring bertambahnya bilangan kuantum utama(n).
Abstract Particle in a box is one of the applications of the Schrodinger equation. Schrodinger equation gives wave function which is used to determine the probability and expectation value of particle in a box. It is also can explain the energy levels of the particle. This study aimed to determine the probability, expectation values, and energy levels of a particle in a three-dimensional box with variations in main quantum numbers in each coordinate axis. The magnitude of the wave function and energy levels are influenced by the main quantum number and the width of the box. The results show that variations in the main quantum number influence the probability of particle in the three-dimensional box except for the width of the box <?CDATA L2\frac{L}{2}2L​?> L 2 and L the probability of particle showing the same value in all variations of the main quantum number. Variations in the main quantum number also influence the expectation value of particle in a three-dimensional box except for the width of the box L the expectation value shows the same value in all variations of the main quantum number. All variations of the main quantum number also influence the magnitude of the energy level of the particle.