Plasma-embedded positronium atom with energy-dependent potential

2021 ◽  
Vol 136 (11) ◽  
Author(s):  
Mustafa Kemal Bahar
Keyword(s):  
Positronium Atom ◽  
Dependent Potential ◽  
Energy Dependent

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

Open Physics ◽  
2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Amar Benchikha ◽  
Lyazid Chetouani
Keyword(s):  
Wave Function ◽  
Spectral Decomposition ◽  
Relativistic Particle ◽  
Wave Functions ◽  
Integral Approach ◽  
Normalizing Constant ◽  
Klein Gordon ◽  
Dependent Potential ◽  
Energy Dependent ◽  
Coulomb Potentials

AbstractThe problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.

scholarly journals Spin (Pseudospin) doublet in view of energy-dependent potential

2017 ◽  
Vol 41 ◽  
pp. 1-12 ◽  
Author(s):  
Mustafa SALTI ◽  
Oktay AYDOĞDU
Keyword(s):  
Dependent Potential ◽  
Energy Dependent

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

Exact solution Dirac equation for an energy-dependent potential

2012 ◽  
Vol 127 (10) ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
R. Oudi ◽  
S. Zarrinkamar ◽  
H. Rahimov
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Dependent Potential ◽  
Energy Dependent

Energy dependent potential in nuclear collisions

1988 ◽  
Vol 484 (2) ◽  
pp. 315-336 ◽  
Author(s):  
D. Bandyopadhyay ◽  
S.K. Samaddar
Keyword(s):  
Nuclear Collisions ◽  
Dependent Potential ◽  
Energy Dependent

scholarly journals On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1161
Author(s):  
Jorge A. Borrego-Morell ◽  
Cleonice F. Bracciali ◽  
Alagacone Sri Ranga
Keyword(s):  
Hilbert Space ◽  
Asymptotic Formula ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Morse Potential ◽  
Bound State ◽  
Orthogonal Basis ◽  
Dependent Potential ◽  
Energy Dependent ◽  
Class Of Functions

We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen–Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen–Morse potential, an identity involving Gegenbauer polynomials is obtained.

Identities for Eigenvalues of the Schrödinger Equation with Energy-Dependent Potential

2011 ◽  
Vol 66 (12) ◽  
pp. 699-704 ◽  
Author(s):  
Chuan Fu Yang
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Eigenvalue Problems ◽  
Schrödinger Operators ◽  
Contour Integration ◽  
Schrodinger Operators ◽  
Separated Boundary Conditions ◽  
Dependent Potential ◽  
Energy Dependent

The present paper deals with eigenvalue problems for the Schrödinger equation with energy dependent potential and some separated boundary conditions. Using the method of contour integration, we obtain some new regularized traces for this class of Schrödinger operators.

The Few-Body Problem in Nonrelativistic Quantum Field Theory

1973 ◽  
Vol 51 (17) ◽  
pp. 1861-1868
Author(s):  
A. Z. Capri
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Body Problem ◽  
Nucleon Nucleon ◽  
Field Theories ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
N Body Problem ◽  
Dependent Potential ◽  
Energy Dependent

We utilize the fact that the nonrelativistic second-quantized formalism is simply a compact way of stating the n-body problem for arbitrary n, to derive the Schrödinger equations for few-body problems. This is particularly useful for models resulting from field theories in which a field is coupled to itself via another field, as in the case of nucleon–nucleon coupling via mesons. In this latter case, one obtains an effective nonlocal, energy dependent potential which itself depends on the possible states of the system.

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