Solution of Schrodinger Equation For Q-Deformed Non-Central Shape Invariant Potential Using Super Symmetry Quantum Mechanics Method

Khaled I. K. Alemgadmi

Published Jan 1, 2015• 0 citations

Abstract

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

Related papers

Analisis Spektrum Energi dan Fungsi Gelombang Persamaan Schrödinger Potensial Non-Sentral Shape Invariance q-Deformasi Menggunakan Metode Nikiforov-Uvarov

Hadma Yuliani, Suparmi Suparmi, C. Cari

Penelitian ini bertujuan untuk menentukan spektrum energi dan fungsi gelombang beberapa potensial non-sentral shape invariance q-deformasi, yaitu potensial Poschl-Teller Termodifikasi plus Scarf, dan potensial Rosen-Morse plus Rosen-Morse menggunakan metode Nikiforov-Uvarov (NU). Penelitian ini merupakan studi literatur untuk menyelesaikan persamaan Schrodinger potensial terdeformasi Poschl-Teller Termodifikasi plus Scarf, dan potensial Rosen-Morse plus Rosen-Morse dengan q-deformasi secara analitik. Spektrum energi dan fungsi gelombang suatu sistem partikel dapat diperoleh dari penyelesaian persamaan Schrodinger. Spektrum energi dan fungsi gelombang potensial non-sentral diperoleh dengan menggunakan metode Nikiforov-Uvarov. Persamaan Schrodinger untuk potensial non sentral q-deformasi secara umum dapat diselesaikan secara eksak bila variabel potensialnya terpisahkan ke bagian radial dan sudut. Spektrum energi untuk potensial ini telah diturunkan secara analitis. Spektrum energi dan fungsi gelombang radial yang diperoleh hanya bersifat pendekatan karena adanya faktor sentrifugal, sedangkan fungsi gelombang bagian sudut dan bilangan kuantum orbital diperoleh dari persamaan Schrodinger bagian sudut 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.

Oct 30, 20162 citations

Analisis Spektrum Energi dan FungsiGelombang Persamaan Schrodinger Untuk Potensial Non-Sentral ShapeInvariance q-deformasi Menggunakan Metode Nikiforof-Uvarov

Hadma Yuliani

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.

Jan 1, 20130 citations

PENYELESAIAN PERSAMAAN SCHRÖDINGER POTENSIAL NON-SENTRAL SCARF HIPERBOLIK PLUS ROSEN-MORSE TRIGONOMETRIK MENGGUNAKAN METODE SUPERSIMETRI MEKANIKA KUANTUM

M. Syaifudin, Suparmi Suparmi, Cari Cari

Abstrak Tujuan dari penelitian ini adalah menyelesaikan persamaan Schrodinger potensial non-sentral Scarf hiperbolik plus Rosen-Morse trigonometrik menggunakan metode Supersimetri Mekanika Kuantum (SUSI MK).Spektrum energi dan fingsi radial diperoleh dari penyelesaian persamaan Schrodinger bagian radial, sedangkan fungsi gelombang bagian sudut dan bilangan kuntum orbital diperoleh dari persamaan Schrodinger bagian sudut polar.Spektrum energi dan bilangan kuantum orbital ditentukan dengan sifat shape invariance .Penentuan fungsi gelombang tingkat dasar bagian radial ditentukan dengan sifat lowering operator dan fungsi gelombang tereksitasi ditentukan dengan sifat raising operator .Baik untuk bagian radial maupun bagian polar ditentukan dengan menggunakan sifat lowering operator dan raising operator . Abstract The purpose of this research is to solve the Schrodinger equation of non-central potential Scarf hyperbolic plus Rosen-Morse trigonometric method Supersymmetry Quantum Mechanics (SUSY QM). Energy spectrum and radial functions derived from the completion of the radial part of the Schrodinger equation, while the wave functions of the corners and orbital quantum numbers obtained from the Schrodinger equation part of the polar angle. Energy spectrum and orbital quantum number is determined by the nature of the shape invariance. Determination of the wave functions of the radial part of the base rate is determined by the nature of lowering operators and the excited wave function is determined by the nature of the raising operator. Both for the radial and polar parts determined by using the properties of lowering and raising operators. Keywords: Schrodinger equation, the non-central potential Scarf hiperbolic plus Rosen-Morse trigonometric, Supersymmetry Quantum Mechanics

Oct 30, 20150 citations

Solusi Analitik Persamaan Schrodinger Terdedeformasi-q dengan Potensial Kratzer dalam Sistem Koordinat Bispherical Menggunakan Metode SUSYQM

Dedy A. Bilaut, C. Cari, Suparmi Suparmi +1 more

Abstract: The analytical solution of the Schrodinger equation affected by Kratzer potential in Bispherical coordinate system was derived. The separable method was applied to reducing the Schrodinger equation which depends on into three one-dimensional Schrodinger equations. The Schrodinger equations as the function of with and without -deformed were solved using the SUSY QM method. The solutions were eigenvalue and eigenfunction of -deformed Schrodinger equation and eigenvalue end eigenfunction of Schrodinger equation with and without q-deformed in Bispherical coordinate system. The energy of the Schrodinger equation with -deformed equals to the Energy of Schrodinger without -deformed since the parameter becomes to zero. Abstrak: Solusi analitik dari Persamaan Schrodinger yang dipengaruhi Potensial Kratzer dalam koordinat Bispherical telah berhasil diturunkan. Metode pemisahan variabel digunakan untuk mereduksi persamaan Schrodinger yang bergantung pada menjadi tiga persamaan Schrodinger satu dimensi. Persamaan Schrodinger fungsi terdeformasi- dan tidak terdeformasi- diselesaikan menggunakan metode SUSY QM. Solusi yang berhasil didapatkan adalah nilai eigen dan fungsi eigen persamaan Schrodinger, masing-masing untuk sistem terdeformasi- dan yang tidak terdeformasi- dalam koordinat Bispherical. Energi dari persamaan Schrodinger terdeformasi- sama dengan energi dari persamaan Schrodinger yang tidak terdeformasi- ketika sama dengan nol.

Prosiding SNFA (Seminar Nasional Fisika dan Aplikasinya)Dec 14, 20201 citation

SOLUSI PERSAMAAN SCHRODINGER D-DIMENSIUNTUK POTENSIAL NON SENTRAL SHAPEINVARIANT DENGAN METODENIKIFOROV-UVAROV

Utama Alan Deta

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.

Jan 1, 20130 citations

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

Khaled I. K. Alemgadmi, Suparmi Suparmi, C. Cari +1 more

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

AIP conference proceedingsJan 1, 20156 citations