scholarly journals EXACT SOLUTIONS OF THE DIRAC EQUATION FOR MODIFIED COULOMBIC POTENTIALS

2000 ◽  
Vol 15 (27) ◽  
pp. 4355-4360
Author(s):  
ANTONIO SOARES DE CASTRO ◽  
JERROLD FRANKLIN
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Linear Combination ◽  
Ground State ◽  
Wave Functions ◽  
Orbital State ◽  
Lorentz Scalar ◽  
Scalar Part

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l=j-½, for any j.

scholarly journals A SIMPLE DIRAC WAVE FUNCTION FOR A COULOMB POTENTIAL WITH LINEAR CONFINEMENT

1999 ◽  
Vol 14 (34) ◽  
pp. 2409-2411 ◽  
Author(s):  
JERROLD FRANKLIN
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Coulomb Potential ◽  
Ground State ◽  
Linear Potential ◽  
Confining Potential ◽  
Lorentz Scalar ◽  
Dirac Wave Function ◽  
Scalar Part

A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength and is not affected by the linear potential. The method works for the ground state, or for the lowest state with l=j-1/2, for any j.

Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential

2016 ◽  
Vol 31 (04) ◽  
pp. 1650017 ◽  
Author(s):  
Shishan Dong ◽  
Qin Fang ◽  
B. J. Falaye ◽  
Guo-Hua Sun ◽  
C. Yáñez-Márquez ◽  
...  
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Ground State ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Potential Parameter ◽  
Heun Functions ◽  
Single Well

We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter [Formula: see text] are illustrated graphically. We find that the potential changes from single well to a double well when parameter [Formula: see text] changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing [Formula: see text] and then becomes negative. We notice that the parities of the wave functions for [Formula: see text] also change.

On the relationship between anharmonic oscillators and perturbed Coulomb potentials in N dimensions

2000 ◽  
Vol 77 (11) ◽  
pp. 863-871 ◽  
Author(s):  
D A Morales ◽  
Z Parra-Mejías
Keyword(s):  
Exact Solutions ◽  
Ground State ◽  
Free Parameter ◽  
Anharmonic Oscillator ◽  
Wave Functions ◽  
Anharmonic Oscillators ◽  
Supersymmetric Partner ◽  
The Relationship ◽  
Coulomb Potentials ◽  
03.65 Ge

The relation between the perturbed Coulomb problem in N dimensionsand the sextic anharmonic oscillator in N' dimensionsis presented and generalized in this work.We show that by performing a transformation, containing a free parameter, on the equations for the two problems we can relate the two systems in dimensions that have not been previously linked. Exact solutions can be obtained for the N-dimensional systems from knownthree-dimensional solutions of the two problems. Using the known ground-state wave functions for these systems, we construct supersymmetric partner potentials that allow us to apply the supersymmetric large-Nexpansion to obtain accurate approximate energy eigenvalues.PACS Nos.: 03.65.Ge, 03.65.Fd, 11.30.Na

DIRAC EQUATION FOR A COULOMB SCALAR, VECTOR AND TENSOR INTERACTION

2011 ◽  
Vol 26 (06) ◽  
pp. 1011-1018 ◽  
Author(s):  
S. ZARRINKAMAR ◽  
H. HASSANABADI ◽  
A. A. RAJABI
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Pseudospin Symmetry ◽  
Spin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Coulomb Term

There is now motivating experimental evidence for relativistic symmetries in nuclei and hadrons, namely pseudospin and spin symmetry limits of the Dirac equation besides the old theoretical backgrounds. The most fundamental ingredients in such studies are definitely the wave functions and energy eigenvalues. Here, having in mind the importance of the Coulomb term as well as the degeneracy-removing role of tensor interaction, we obtain the exact solutions to the problem for Coulomb scalar, vector and tensor terms in both spin and pseudospin symmetry limits. We see that, contrary to many other common cumbersome techniques, the problem is simply solved via the methodology of supersymmetric quantum mechanics.

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

Exact solutions of Dirac equation

Pramana ◽  
1979 ◽  
Vol 12 (5) ◽  
pp. 475-480 ◽  
Author(s):  
S V Kulkarni ◽  
L K Sharma
Keyword(s):  
Dirac Equation ◽  
Exact Solutions

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

Exact solutions of Dirac equation on a static curved space–time

2019 ◽  
Vol 401 ◽  
pp. 21-39 ◽  
Author(s):  
M.D. de Oliveira ◽  
Alexandre G.M. Schmidt
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Space Time ◽  
Curved Space
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