Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

2014 ◽  
Author(s):  
C. Cari ◽  
A. Suparmi
Keyword(s):  
Dirac Equation ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Noncentral Potential

Bound state solution of the Dirac equation for a new anharmonic oscillator potential

2007 ◽  
Vol 76 (5) ◽  
pp. 442-444 ◽  
Author(s):  
Gao-Feng Wei ◽  
Chao-Yun Long ◽  
Zhi He ◽  
Shui-Jie Qin ◽  
Jing Zhao
Keyword(s):  
Dirac Equation ◽  
Anharmonic Oscillator ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Oscillator Potential ◽  
Anharmonic Oscillator Potential

EXACT SOLUTION OF THE DIRAC EQUATION FOR A SINGULAR CENTRAL POWER POTENTIAL

2000 ◽  
Vol 15 (25) ◽  
pp. 1583-1588 ◽  
Author(s):  
SUBIR K. BOSE ◽  
AXEL SCHULZE-HALBERG
Keyword(s):  
Exact Solution ◽  
Excited State ◽  
Dirac Equation ◽  
Power Law ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Coulomb Term ◽  
Coulomb Part

We compute an exact solution of the Dirac equation for a certain power law potential that consists of two parts: a scalar and a vector, where the latter contains a Coulomb term. We obtain energies that turn out to depend only on the strength of the Coulomb part of the potential, but not on the remaining power law part. We show that our ansatz also yields a bound state solution for the lowest excited state. This work is an extension of Franklins result.7

scholarly journals Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Eser Olğar ◽  
Hayder Dhahir ◽  
Haydar Mutaf
Keyword(s):  
Dirac Equation ◽  
Coulomb Potential ◽  
Mass Function ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Solution ◽  
Function Generator ◽  
Dependent Mass ◽  
And Function ◽  
Position Dependent Mass

AbstractThe bound state solution of Coulomb Potential in the Dirac equation is calculated for a position dependent mass function M(r) within the framework of the asymptotic iteration method (AIM). The eigenfunctions are derived in terms of hypergeometric function and function generator equations of AIM.

Existence of a bound state solution for quasilinear Schrödinger equations

2017 ◽  
Vol 8 (1) ◽  
pp. 323-338 ◽  
Author(s):  
Yan-Fang Xue ◽  
Chun-Lei Tang
Keyword(s):  
Nonlinear Term ◽  
Quasilinear Equation ◽  
Bound State ◽  
State Solution ◽  
Schrodinger Equations ◽  
Linking Theorem ◽  
Schrödinger Equations ◽  
Bound State Solution ◽  
Asymptotically Linear ◽  
Semilinear Equation

Abstract In this article, we establish the existence of bound state solutions for a class of quasilinear Schrödinger equations whose nonlinear term is asymptotically linear in {\mathbb{R}^{N}} . After changing the variables, the quasilinear equation becomes a semilinear equation, whose respective associated functional is well defined in {H^{1}(\mathbb{R}^{N})} . The proofs are based on the Pohozaev manifold and a linking theorem.

scholarly journals Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff-Type Problems with a General Critical Nonlinearity

2018 ◽  
Vol 61 (4) ◽  
pp. 1023-1040 ◽  
Author(s):  
Jianjun Zhang ◽  
David G. Costa ◽  
João Marcos do Ó
Keyword(s):  
Positive Solutions ◽  
Local Minimum ◽  
Type Equation ◽  
Bound State ◽  
State Solution ◽  
Critical Nonlinearity ◽  
Bound State Solution ◽  
Kirchhoff Type ◽  
Image Position ◽  
Kirchhoff Type Problems

AbstractWe are concerned with the following Kirchhoff-type equation$$ - \varepsilon ^2M\left( {\varepsilon ^{2 - N}\int_{{\open R}^N} {\vert \nabla u \vert^2{\rm d}x} } \right)\Delta u + V(x)u = f(u),\quad x \in {{\open R}^N},\quad N{\rm \ges }2,$$whereM ∈ C(ℝ+, ℝ+),V ∈ C(ℝN, ℝ+) andf(s) is of critical growth. In this paper, we construct a localized bound state solution concentrating at a local minimum ofVasε → 0 under certain conditions onf(s),MandV. In particular, the monotonicity off(s)/sand the Ambrosetti–Rabinowitz condition are not required.

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