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Study of Dzarrah: Analysis of Wave Functions Potential Non Central Coulombic Rosen Morse

Cecilia Yanuarief

Published Apr 28, 2019• 0 citations
Publisher

Abstract

It has been obtained a graph of the wave function of Coulombic's non-central potential Schrodinger equation Rosen Morse which is systematically an embodiment of hydrogen atoms and their isotopes. Schrodinger's equation is solved through variable spatial techniques with each variable resolved using a different method so that the radial and angular part wave functions are visualized by Matlab-based computer programming. Visualization of the radial wave function that is formed describes the probability value of the discovery of electrons which are small parts of an atom, while the visualization of the formed angular wave function shows the movement of electrons in an energy level. The mention of the atom itself is already in the Qur'an, Allah says in surah As-Saba verse 3. According to the interpretation of Quraish Shihab the word dzarrah in Arabic refers to a very small object, the size of an ant's child or fine dust. The phrase mitsqalu dzarrah in this verse means the weight of an atom. This implies the presence of a compound whose specific gravity is lighter than an atom.

DOI
10.14421/kaunia.1411

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ABSTRACTThe objectives of this research are to determine energy spectra and wavefunction of schrodinger equation for q-deformed Rosen Morse plus non centraltrigonometric q-deformed Posch Teller potential and hyperbolic q-deformed Scarfplus Non central q-deformed Rosen Morse Trigonometric Potential using SUSY QMApproach. Actually, SUSY QM propose that the boson can change into fermion viceversa. However, the evidence of this phenomena does not exist in this world. Wittenproposed that SUSY must be broken. This SUSY theoretically can be solve most ofproblems in Quantum Mechanics. After the energy spectra and wave functionfounded, we will plot a graph simulation to understand the effect of potentials inenergy spectra and wave function of system.Keywords: Schrodinger Equation, q-Deformed Non-Central Shape InvariantPotential, and Supersymmetry of Quantum MechanicsABSTRAKTujuan dari penelitian ini adalah untuk menentukan spektrum energi danfungsi gelombang persamaan Schrodinger untuk q-deformasi Rosen Morse ditambahnon sentral trigonometri q-deformasi Poschl Teller potensial dan hiperbolik q-cacatScarf ditambah Non pusat q-deformasi Rosen Morse trigonometri Potensimenggunakan SUSY Pendekatan QM. Sebenarnya SUSY QM mengusulkan bahwaboson bisa berubah menjadi fermion sebaliknya. Namun, bukti fenomena ini tidakada di dunia ini. Witten mengusulkan agar SUSY harus rusak. SUSY ini secarateoritis dapat dipecahkan sebagian besar masalah di Kuantum Mekanika. Setelahspektrum energi dan gelombang fungsi didirikan, kita akan plot simulasi grafik untukmemahami efek dari potensi dalam spektrum energi dan fungsi gelombang sistem.Kata kunci: Schrodinger Equation, q-Deformasi non-Central Shape InvariantPotensial, dan Supersymmetri of Kuantum Mechanics

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It has been obtained a graph of the wave function of Coulombic's non-central potential Schrodinger equation Rosen Morse which is systematically an embodiment of hydrogen atoms and their isotopes. Schrodinger's equation is solved through variable spatial techniques with each variable resolved using a different method so that the radial and angular part wave functions are visualized by Matlab-based computer programming. Visualization of the radial wave function that is formed describes the probability value of the discovery of electrons which are small parts of an atom, while the visualization of the formed angular wave function shows the movement of electrons in an energy level. The mention of the atom itself is already in the Qur'an, Allah says in surah As-Saba verse 3. According to the interpretation of Quraish Shihab the word dzarrah in Arabic refers to a very small object, the size of an ant's child or fine dust. The phrase mitsqalu dzarrah in this verse means the weight of an atom. This implies the presence of a compound whose specific gravity is lighter than an atom.
Research has been conducted which shows the quantization visualization of hydrogen atom orbitals angular space in Rosen Morse potential system interference when the electrons are excited in the state of nr= 2 and l = 1 through the polar function analysis of the Schrödinger Potential of Non-Central Coloumbic Rosen Morse. The polar Schrödinger equation is solved using the Romanovski polynomial method to obtain the polar wave function. To show the accuracy of the analysis, the polar wave function spectrum i s visualized with Matlab-based computer programming.
The purposes of the research were to determine the energy spectrum and wave function of some q-deformed non-central shape invariance potentials, Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus Rosen-Morse potential using Nikiforov-Uvarov Method. The research was a literature study to solve Schrodinger equation for qdeformed Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus Rosen-Morse potential analytically. The energy spectrum and the wave functions of a system particles can be determined by Schrodinger equation. The energy spectrum and wave function for q-deformed non-central potential determined by Nikiforov-Uvarov method. Generally, the Schrodinger equation for the noncentral potential can be solved by exact if the potential variables separated into the radial and angular part. The energy spectrum and the radial wave function obtained approximately due to the centrifugal term from the radial Schrodinger equation, while the angular wave function and the orbital quantum number are obtained from angular part of Schrodinger equation. Key words: The Energy Spectrum, Wave Function, Schrodinger Equation, Non- Central, q-deformed, Nikiforov-Uvarov Method.
This research’s aim are to determine energy spectra and wave function of Schrodinger Equation in D-Dimensions for non central shape invariant potentials, that is, Scarf hyperbolic plus non central Poschl-Teller potential and Scarf trigonometric plus non central Rosen-Morse potential with Nikivarof-Uvarov method. Nikivarof-Uvarov method are the method for solving a second order of differential equation which transform that equation into hypergeometric equation using a correct subtitution of variable. Research was done through a literature studies to solve the Schrodinger equation D-Dimensions analitically for Scarf hyperbolic plus non central Poschl- Teller potential and Scarf trigonometric plus non central Rosen-Morse potential. Energy spectra and wave function obtained by Nikivarof-Uvarov method. After obtaining energy levels and compared with the other methods in the special conditions, the wave function can be obtained by Nikivarof-Uvarov method. Energy spectra of the Scarf hyperbolic plus non-central Poschl Teller potential and Scarf trigonometric plus non-central Rosen Morse potential on DDimensions which obtained by Nikiforov-Uvarof methods have a results consistently with previous research on special condition. Energy spectra and wave functions of both combination of potentials are determined approximately for the value of orbital quantum number l ≠ 0. Keywords: Schrodinger Equation in D-Dimensions, Non Central Shape Invariant Potentials, and Nikivarof-Uvarov Method.
The simplest atom consisting of a proton and an electron is a hydrogen atom. The energy level and the probability of finding an electron in a hydrogen atom can be determined based on the function of radial wave. The function of radial wave of a hydrogen atom is influenced by the principal quantum number ( n ) and the orbital quantum number ( l ). Completion of the function of radial wave of a hydrogen atom in the principal quantum numbers( n ) 4 and 5 uses the time-independent Schrodinger equation approach in spherical coordinates, variable separation method and uses the associated Laguerre function. The normalized of the function of radial wave of a hydrogen atom R nl ( r ) at n = 4 produces four wave functions:R 40 ( r ); R 41 ( r ); R 42 ( r ); R 43 ( r ), whereas at n = 5 produces five wave functions:R 50 ( r ); R 51 ( r ); R 52 ( r ); R 53 ( r ); R 54 ( r ). The results of this research in the form of the functions of radial wave of hydrogen atom can be used to determine the behavior of electron in a hydrogen atom.
The aims of the research are to determine energy spectra and radial wave function of Quantum system in D-Dimensions for Eckart plus Manning Rosen potential with Nikiforov-Uvarov method. NikiforovUvarov method is method for solving a second-order of differential equations by transforming the equation into the hypergeometric equation by the method of separation of intermediate variables by appropriate variable substitution. The analytical results is energy spectra and radial wave function visualization by Microsoft Excel 2010 and Mathematical Laboratory 2013 Programing. The visualization result can be showed that the orbital quantum number increase and the dimension increase causing the bounding energy decrease in the –n spectra energy. The probability visualization for ground state condition result can be showed that the orbital increase, so probability decrease, while the dimension increase for ground state condition is decreasing probability.
ABSTRACTThe objectives of this research are to determine energy spectra and wavefunction of schrodinger equation for q-deformed Rosen Morse plus non centraltrigonometric q-deformed Posch Teller potential and hyperbolic q-deformed Scarfplus Non central q-deformed Rosen Morse Trigonometric Potential using SUSY QMApproach. Actually, SUSY QM propose that the boson can change into fermion viceversa. However, the evidence of this phenomena does not exist in this world. Wittenproposed that SUSY must be broken. This SUSY theoretically can be solve most ofproblems in Quantum Mechanics. After the energy spectra and wave functionfounded, we will plot a graph simulation to understand the effect of potentials inenergy spectra and wave function of system.Keywords: Schrodinger Equation, q-Deformed Non-Central Shape InvariantPotential, and Supersymmetry of Quantum MechanicsABSTRAKTujuan dari penelitian ini adalah untuk menentukan spektrum energi danfungsi gelombang persamaan Schrodinger untuk q-deformasi Rosen Morse ditambahnon sentral trigonometri q-deformasi Poschl Teller potensial dan hiperbolik q-cacatScarf ditambah Non pusat q-deformasi Rosen Morse trigonometri Potensimenggunakan SUSY Pendekatan QM. Sebenarnya SUSY QM mengusulkan bahwaboson bisa berubah menjadi fermion sebaliknya. Namun, bukti fenomena ini tidakada di dunia ini. Witten mengusulkan agar SUSY harus rusak. SUSY ini secarateoritis dapat dipecahkan sebagian besar masalah di Kuantum Mekanika. Setelahspektrum energi dan gelombang fungsi didirikan, kita akan plot simulasi grafik untukmemahami efek dari potensi dalam spektrum energi dan fungsi gelombang sistem.Kata kunci: Schrodinger Equation, q-Deformasi non-Central Shape InvariantPotensial, dan Supersymmetri of Kuantum Mechanics