scholarly journals Analysis of minimal length effect on the non-relativistic energy and wave function for the exponential type potential using Supersymmetric Quantum Mechanics

2018 ◽  
Vol 997 ◽  
pp. 012017 ◽  
Author(s):  
H Azizah ◽  
A Suparmi ◽  
C Cari
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Exponential Type ◽  
Minimal Length ◽  
Supersymmetric Quantum Mechanics ◽  
Relativistic Energy ◽  
Length Effect ◽  
Type Potential

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Tao ◽  
Peng Wang ◽  
Haitang Yang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Statistical Physics ◽  
Turning Point ◽  
Minimal Length ◽  
Jacobi Method ◽  
Homogeneous Field ◽  
Quantization Rule ◽  
Connection Formula ◽  
Forbidden Region

In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up toOβ2. We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.

Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

2010 ◽  
Author(s):  
Lily Maysari Angraini ◽  
Suparmi ◽  
Viska Inda Variani ◽  
Khairurrijal ◽  
Mikrajuddin Abdullah ◽  
...  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Supersymmetric Quantum Mechanics

CONDITIONALLY EXACTLY SOLVABLE SINGULAR EVEN POWER POTENTIAL IN SUPERSYMMETRIC QUANTUM MECHANICS

2002 ◽  
Vol 17 (21) ◽  
pp. 1367-1375 ◽  
Author(s):  
BARNALI CHAKRABARTI ◽  
TAPAN KUMAR DAS
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Riccati Equation ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
New Technique ◽  
Body System ◽  
Operator Formalism ◽  
Shape Invariance ◽  
Exactly Solvable

We solve strongly singular even power potential with inverse quadratic, inverse quartic and inverse sextic terms, using superpotential ansatz technique. We show that our new technique is very powerful and simple compared to traditional wave function ansatz technique. We also point out conditional shape invariance as the underlying symmetry to get conditional exactness. We also generalize the case for two-body Hamiltonian and propose an alternative way to solve Riccati equation instead of solving Schrödinger equation. We present operator formalism which is rather powerful. We also discuss the problem encountered in generalizing the potential for an N-body system.

scholarly journals INDUCED VARIATIONAL METHOD FROM SUPERSYMMETRIC QUANTUM MECHANICS AND THE SCREENED COULOMB POTENTIAL

2000 ◽  
Vol 15 (19) ◽  
pp. 1253-1259 ◽  
Author(s):  
ELSO DRIGO FILHO ◽  
REGINA MARIA RICOTTA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Variational Method ◽  
Coulomb Potential ◽  
Trial Wave Function ◽  
Supersymmetric Quantum Mechanics ◽  
Exact Results ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

scholarly journals Analytical solution of the Bohr-Mottelson equation in minimal length effect for cotangent hyperbolic potential using the hypergeometric method

2018 ◽  
Vol 2 (1) ◽  
pp. 12
Author(s):  
Siti Noor Fatimah ◽  
A. Suparmi ◽  
C. Cari ◽  
Isnaini Lilis Elviyanti
Keyword(s):  
Wave Function ◽  
Energy Spectrum ◽  
Analytical Solution ◽  
Minimal Length ◽  
Wave Functions ◽  
Minimum Length ◽  
Length Effect ◽  
Matlab Software ◽  
Hyperbolic Potential ◽  
Deformed Nucleus

The rigid deformed nucleus of minimal length effect is investigated using the Bohr-Mottelson equation that influenced by cotangent hyperbolic potential. The Bohr-Mottelson equation in effect a minimum length resolved hypergeometric method for determining the energy spectrum and the wave functions. Energy spectrum was calculated using Matlab software and the wave function is displayed in the form of hypergeometric.

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