Wave functions for weakly coupled bound states

1982 ◽  
Vol 25 (5) ◽  
pp. 2467-2472 ◽  
Author(s):  
S. H. Patil
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Weakly Coupled

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

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.

scholarly journals Universality of excited three-body bound states in one dimension

2021 ◽  
Author(s):  
Lucas Happ ◽  
Matthias Zimmermann ◽  
Maxim A Efremov
Keyword(s):  
Excited States ◽  
Bound States ◽  
Space Dimension ◽  
Binding Energies ◽  
Wave Functions ◽  
One Dimension ◽  
Strong Indication ◽  
Body System ◽  
Weakly Bound ◽  
Three Body

Abstract We study a heavy-heavy-light three-body system confined to one space dimension in the regime where an excited state in the heavy-light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.

THE BETHE–SALPETER EQUATION APPROACH TO BOUND STATE: SCALAR–FERMION CASE AND SCALAR–SCALAR CASE

2007 ◽  
Vol 22 (39) ◽  
pp. 2979-2992 ◽  
Author(s):  
JIAO-KAI CHEN ◽  
ZHENG-XIN TANG ◽  
QING-DONG CHEN
Keyword(s):  
Bound States ◽  
Bound State ◽  
Wave Functions ◽  
Scalar Case ◽  
Equation Approach

The general form of the Bethe–Salpeter wave functions for bound states comprising one scalar constituent and one fermion, or two scalars is presented. Using the reduced Salpeter equation obtained, we can work out the effective nonrelativistic potentials. And one new version of reduced Bethe–Salpeter equation is proposed by extending Gross approximation.

Dirac Equation with Mixed Scalar–Vector–Pseudoscalar Linear Potential under Relativistic Symmetries

2015 ◽  
Vol 70 (9) ◽  
pp. 713-720 ◽  
Author(s):  
Hadi Tokmehdashi ◽  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Linear Potential ◽  
Energy Eigenvalues ◽  
Nu Method

AbstractIn the presence of spin and pseudospin (p-spin) symmetries, the approximate analytical bound states of the Dirac equation, which describes the motion of a spin-1/2 particle in 1+1 dimensions for mixed scalar–vector–pseudoscalar linear potential are investigated. The Nikiforov–Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in their closed forms.

WKB method for potentials unbounded from below

2016 ◽  
Vol 30 (03) ◽  
pp. 1650003 ◽  
Author(s):  
Aleksandar Demić ◽  
Vitomir Milanović ◽  
Jelena Radovanović ◽  
Milenko Musić
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Wave Functions ◽  
Wkb Method ◽  
Symmetric Potential ◽  
Overlap Integral ◽  
Entire Spectrum ◽  
One Dimensional ◽  
Model Based ◽  
Exactly Solvable

Bound states degenerated in energy (and differing in parity) may form in one-dimensional quantum mechanics if the potential is unbounded from below. We focus on symmetric potential and present quasi-exactly solvable (QES) model based on WKB method. The application of this method is limited on slow-changing potentials. We consider the overlap integral of WKB wave functions [Formula: see text] and [Formula: see text] which correspond to energies [Formula: see text] and [Formula: see text], and by setting [Formula: see text], we determine the type of spectrum depending on parameter [Formula: see text] which arises from this method. For finite value [Formula: see text], we show that the entire spectrum will consist of degenerated bound states.

Dynamical variables in the Bethe-Salpeter formalism

1955 ◽  
Vol 233 (1193) ◽  
pp. 248-266 ◽  
Keyword(s):  
Matrix Element ◽  
Bound States ◽  
Dynamical Variable ◽  
Wave Functions ◽  
Coupling Constant ◽  
Scattering States ◽  
The Matrix ◽  
The Masses

It is shown that a knowledge of the behaviour of the propagators around their singularities enables one to determine not only the masses of bound states, but also the matrix element of any dynamical variable between two bound states. One is thus enabled to find such a matrix element, to any order in the coupling constant, by the integration of certain expressions over the corresponding Bethe-Salpeter wave-functions. As a consequence, it is possible to find normalization and orthogonality properties of these wave-functions, which in turn lead to the condition which must be imposed on their singularities a t the origin. More light is thus shed on Goldstein’s difficulty concerning the existence of a continuous infinity of bound states. The formalism is extended to scattering states in which some of the particles may be composite—in particular, an expression for the S -matrix is obtained

Dirac Bound States of the Killingbeck Potential Under External Magnetic Fields

2015 ◽  
Vol 70 (7) ◽  
pp. 499-505 ◽  
Author(s):  
Zahra Sharifi ◽  
Fateme Tajic ◽  
Majid Hamzavi ◽  
Sameer M. Ikhdair
Keyword(s):  
Wave Function ◽  
Magnetic Fields ◽  
Ground State ◽  
Bound States ◽  
State Energy ◽  
Potential Model ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Ansatz Method

AbstractThe Killingbeck potential model is used to study the influence of the external magnetic and Aharanov–Bohm (AB) flux fields on the splitting of the Dirac energy levels in a 2+1 dimensions. The ground state energy eigenvalue and its corresponding two spinor components wave functions are investigated in the presence of the spin and pseudo-spin symmetric limit as well as external fields using the wave function ansatz method.

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