Lévy-Schrödinger Equation: Their Eigenvalues and Eigenfunctions Using Sinc Methods

2020 ◽  
pp. 55-98
Author(s):  
Gerd Baumann
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Eigenvalues And Eigenfunctions ◽  
Sinc Methods

EIGENSTATES OF THE GRAVITATIONAL SCHRÖDINGER EQUATION

1998 ◽  
Vol 13 (29) ◽  
pp. 2327-2336 ◽  
Author(s):  
DAVID H. BERNSTEIN ◽  
ELDAR GILADI ◽  
KINGSLEY R. W. JONES
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Spectrum ◽  
Einstein Condensate ◽  
Shooting Methods ◽  
S Wave ◽  
Eigenvalues And Eigenfunctions ◽  
Bose Einstein Condensate ◽  
Outer Iteration ◽  
Bose Einstein

We develop a new algorithm to compute the eigenvalues and eigenfunctions of the gravitational Schrödinger equation. The nonlinear two-point boundary problem is solved by an inner–outer iteration and the resulting method is fast, readily parallelizable, and, unlike shooting methods, is able to compute eigenfunctions with a very large number (>50) of nodes. The theory and implementation of the method are discussed and it is applied to compute the s-wave spectrum of a gravitational Bose–Einstein condensate.

scholarly journals Charmonium Properties Using the Discrete Variable Representation (DVR) Method

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Bhaghyesh A.
Keyword(s):  
Numerical Methods ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hamiltonian Matrix ◽  
Discrete Variable ◽  
Discrete Variable Representation ◽  
Eigenvalues And Eigenfunctions ◽  
Decay Widths ◽  
Variable Representation ◽  
Good Agreement

The Schrödinger equation is solved numerically for charmonium using the discrete variable representation (DVR) method. The Hamiltonian matrix is constructed and diagonalized to obtain the eigenvalues and eigenfunctions. Using these eigenvalues and eigenfunctions, spectra and various decay widths are calculated. The obtained results are in good agreement with other numerical methods and with experiments.

scholarly journals Solution Of Schrödinger Equation For Poschl-Teller Plus Scarf Non-Central Potential Using Supersymmetry Quantum Mechanics Aproach

2015 ◽  
Vol 4 (1) ◽  
pp. 25-35
Author(s):  
Antomi Saregar
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Eigenvalues And Eigenfunctions ◽  
Central Potential ◽  
Energy Eigenvalues ◽  
State Wave ◽  
Shape Invariant ◽  
Raising Operator ◽  
Invariant Properties

In this paper, we show that the exact energy eigenvalues and eigenfunctions of the Schrödinger equation for charged particles moving in a certain class of noncentral potentials can be easily calculated analytically in a simple and elegant manner by using Supersymmetric method (SUSYQM). We discuss the Poschl-Teller plus Scarf non-central potential systems. Then, by operating the lowering operator we get the ground state wave function, and the excited state wave functions are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the closed form obtained using the shape invariant properties. The results are in exact agreement with other methods.Keyword: supersymmetry, non-central potentials, poschl teller plus scarf.

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Jacobi Polynomials ◽  
Wave Functions ◽  
Three Dimensions ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Pseudoharmonic Potential ◽  
Uvarov Method

AbstractA new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.

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

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