Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

PILLAR OF PHYSICS

PERHITUNGAN TINGKAT ENERGI SUMUR POTENSIAL KEADAAN TERIKAT MELALUI PERSAMAAN SCHRODINGER MENGGUNAKAN METODE BEDA HINGGA

Hanifah Rahmayani

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Schrodinger equations are widely used in solving a variety of problems, one of them is particles in a box in especially of potential wells bound state. Particle in a box is a discrete circumstances, so we must examined whether or not the degeneration of these particles. The Schrodinger equation analysed to get a form of modeling of energy levels and wave functions in potential wells of the circumstance used numerical method. We also can show energy level of each state from the model. The numerical approaches is finnite difference method using  Matlab R2010 software. Numerical calculation shows k value. k 1 and k 3 gets from solution of cos equation, whereas k 2 and k 4 gets from solution of sin equation. The k value is used to know the energy level in potential wells. energy level model show wave fucntion. In potential well bound state, Energy level and wave functions be smaller when potential energy is high and it is high when potential when potential energy is small. When wide of potential well is smaller, energy level and wave function be smaller too. But there isn’t show energy level and wave function when wide of potential well is high. The shape of energy level and and wave function of particle in box.

Related papers

Solving Numerically Schrödinger Equation for Confined Particle in the Finite Potential Well

B. Bounthong

The quantum model of finite potential well is a most subject in the book of quantum mechanics. The solutions maybe derive from one dimension Schrödinger’s equation for describe a bound state energy of confined particle in the finite potential well. Sometime, the problem of confined particle in the finite potential well does not have an exact solution yet, but there are in fact exact solution.In this work a numerical technique is adopted to find the exact solution for the quantum model of finite potential well. To achieve this numerical solution, I use Fortran code computer program by the Newton-Raphson method for calculating the Eigen state energy for a particle (electron) confined in the finite potential well. Five values of potential width and depth have studied, the results showed that large potential width and large potential depth led me to more bound states, while smaller potential width and depth led me to fewer bound states.A comparison between infinite potential and finite potential has been presented. The results bound state energy and penetration. The results of comparison showed that the wave function of particle confined in the infinite potential cannot penetrate in the well, while the wave function of particle in the finite potential was penetrate in the well; the energy levels of an infinite well are much higher than that the corresponding energy levels for finite potential well. For confined particle in 2 or 3-dimension, we can reduce from result of 1-dimension.

Vālasān vithanyāsāt mahāvithanyālai Suphānuvong.•Jun 20, 2022•0 citations

Even-exponent potential wells solved by the finite difference method

Tisorn Na Phattalung, Wittaya Kanchanapusakit

Abstract This article examines a particle in a one-dimensional potential well V a (x) ∝ x a , where a ≥ 2 is an even integer. The system is referred to as a harmonic oscillator when a = 2 and as a particle in a box when a → ∞. The finite difference method is applied to solve the Schrödinger equation, determining the ground-state energies and wave functions. Giving accurate description in the cases of a = 2 and a → ∞, the numerical method allows us to explore the system for intermediate values of a, revealing how the energies and wave functions evolve between these two limits. The study includes discussions on the virial theorem, the uncertainty principle, excited states, and the limitation of the numerical method.

Physica Scripta•Mar 19, 2025•0 citations

Solving Schrödinger Equation for Finite Potential Well Using the Iterative Method

Laith Abdul Aziz Al-Ani, Russul K. Abid

The quantum Finite Square Well (FSW) model is a well-known topic in most quantum mechanics (QM) books.A couple of equations can be derived from one dimensional Schrodinger equation for a finite potential well for describing the bound Eigen states within the well.Sometimes the FSW problem does not have an exact solution, yet, there are in fact exact solutions.In this work a computational techniques is adopted to find the exact solution for FSW.To achieve this computational solution, a computer program has been written in Basic language for calculating the Eigen state energy for a particle confined in finite potential well using the iterative method (IM).Six values of potential width have been studied with potential depth.The results showed that wider potential width led us to more bound states, while narrower potential width led us to less bound states.Six values of potential depth have been studied with potential width.The results showed that larger potential depth led us to more bound states, while smaller potential width led us to less bound states.A Comparison Between Finite and Infinite Potential Well has been also presented.The result of comparison showed that energy levels of an infinite well are much higher than that the corresponding energy levels for finite potential well.In general, the matching between the results of the iterative method and the graphical method (GM) proving that the iteration method can be regarded as a useful tool for describing the solutions of the 1-dimensional FSW problem.

Journal of Al-Nahrain University-Science•Dec 1, 2019•2 citations

Determination of energy levels, probabilities, and expectation values of particles in the three-dimensional box at quantum numbers ≤5

Bambang Supriadi, Zainur Rasyid Ridlo, Nur Aida +3 more

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 .

Journal of Physics Conference Series•Apr 1, 2019•3 citations

ANALISIS DAN VISUALISASI PERSAMAAN KLEIN-GORDON PADA ELEKTRON DALAM SUMUR POTENSIAL DENGAN MENGGUNAKAN PROGRAM MATHEMATIC 10

Syahrul Humaidi, Tua Raja Simbolon, Russell Ong +1 more

Schrödinger equation is a wave equation that describes the behaviour of an electron including determining its energy levels. However, when the motion of electrons was assumed as relativistic motion(vc), then the schrödinger equation must be changed into Klein-Gordon equation(relativistic Schrödinger equation). In order to compare both equations, we analyzed and visualized the Klein-Gordon equation for an electron in a potential well with Wolfram Mathematica 10 software. The visualization from Mathematica 10 gave the same wavefunction graphs and probability density graphs as the Schrödinger equation. The difference is only in the visualization of energy levels graphs. Keywords:Klein-Gordon equation, Mathematica 10, electron, energy levels.

Prosiding SNF (Seminar Nasional Fisika)•Jan 1, 2016•0 citations

Criteria for bound-state solutions in quantum mechanics

Carl A. Kocher

When does the Schrödinger equation have bound-state solutions? This question is pursued by a variational method with simple trial wave functions. An arbitrary one- or two-dimensional attractive potential is shown to have at least one discrete energy level, and estimates of the binding energy are obtained for shallow potential wells. In other problems, sufficient conditions are established for the existence of bound states.

American Journal of Physics•Jan 1, 1977•22 citations
Schrodinger equations are widely used in solving a variety of problems, one of them is particles in a box in especially of potential wells bound state. Particle in a box is a discrete circumstances, so we must examined whether or not the degeneration of these particles. The Schrodinger equation analysed to get a form of modeling of energy levels and wave functions in potential wells of the circumstance used numerical method. We also can show energy level of each state from the model. The numerical approaches is finnite difference method using  Matlab R2010 software. Numerical calculation shows k value. k 1 and k 3 gets from solution of cos equation, whereas k 2 and k 4 gets from solution of sin equation. The k value is used to know the energy level in potential wells. energy level model show wave fucntion. In potential well bound state, Energy level and wave functions be smaller when potential energy is high and it is high when potential when potential energy is small. When wide of potential well is smaller, energy level and wave function be smaller too. But there isn’t show energy level and wave function when wide of potential well is high. The shape of energy level and and wave function of particle in box.
The quantum model of finite potential well is a most subject in the book of quantum mechanics. The solutions maybe derive from one dimension Schrödinger’s equation for describe a bound state energy of confined particle in the finite potential well. Sometime, the problem of confined particle in the finite potential well does not have an exact solution yet, but there are in fact exact solution.In this work a numerical technique is adopted to find the exact solution for the quantum model of finite potential well. To achieve this numerical solution, I use Fortran code computer program by the Newton-Raphson method for calculating the Eigen state energy for a particle (electron) confined in the finite potential well. Five values of potential width and depth have studied, the results showed that large potential width and large potential depth led me to more bound states, while smaller potential width and depth led me to fewer bound states.A comparison between infinite potential and finite potential has been presented. The results bound state energy and penetration. The results of comparison showed that the wave function of particle confined in the infinite potential cannot penetrate in the well, while the wave function of particle in the finite potential was penetrate in the well; the energy levels of an infinite well are much higher than that the corresponding energy levels for finite potential well. For confined particle in 2 or 3-dimension, we can reduce from result of 1-dimension.
Abstract This article examines a particle in a one-dimensional potential well V a (x) ∝ x a , where a ≥ 2 is an even integer. The system is referred to as a harmonic oscillator when a = 2 and as a particle in a box when a → ∞. The finite difference method is applied to solve the Schrödinger equation, determining the ground-state energies and wave functions. Giving accurate description in the cases of a = 2 and a → ∞, the numerical method allows us to explore the system for intermediate values of a, revealing how the energies and wave functions evolve between these two limits. The study includes discussions on the virial theorem, the uncertainty principle, excited states, and the limitation of the numerical method.
The quantum Finite Square Well (FSW) model is a well-known topic in most quantum mechanics (QM) books.A couple of equations can be derived from one dimensional Schrodinger equation for a finite potential well for describing the bound Eigen states within the well.Sometimes the FSW problem does not have an exact solution, yet, there are in fact exact solutions.In this work a computational techniques is adopted to find the exact solution for FSW.To achieve this computational solution, a computer program has been written in Basic language for calculating the Eigen state energy for a particle confined in finite potential well using the iterative method (IM).Six values of potential width have been studied with potential depth.The results showed that wider potential width led us to more bound states, while narrower potential width led us to less bound states.Six values of potential depth have been studied with potential width.The results showed that larger potential depth led us to more bound states, while smaller potential width led us to less bound states.A Comparison Between Finite and Infinite Potential Well has been also presented.The result of comparison showed that energy levels of an infinite well are much higher than that the corresponding energy levels for finite potential well.In general, the matching between the results of the iterative method and the graphical method (GM) proving that the iteration method can be regarded as a useful tool for describing the solutions of the 1-dimensional FSW problem.
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 .
Schrödinger equation is a wave equation that describes the behaviour of an electron including determining its energy levels. However, when the motion of electrons was assumed as relativistic motion(vc), then the schrödinger equation must be changed into Klein-Gordon equation(relativistic Schrödinger equation). In order to compare both equations, we analyzed and visualized the Klein-Gordon equation for an electron in a potential well with Wolfram Mathematica 10 software. The visualization from Mathematica 10 gave the same wavefunction graphs and probability density graphs as the Schrödinger equation. The difference is only in the visualization of energy levels graphs. Keywords:Klein-Gordon equation, Mathematica 10, electron, energy levels.