Core size effects, bound states, and scattering states of the Aharonov–Bohm problem

1985 ◽  
Vol 26 (9) ◽  
pp. 2218-2221 ◽  
Author(s):  
N. Gauthier ◽  
P. Rochon
Keyword(s):  
Size Effects ◽  
Bound States ◽  
Core Size ◽  
Scattering States ◽  
Aharonov Bohm

scholarly journals Effective Interactions of Relativistic Composite Particles in Unified Nonlinear Spinor-Field Models. I

1985 ◽  
Vol 40 (1) ◽  
pp. 14-28
Author(s):  
H. Stumpf
Keyword(s):  
Spinor Field ◽  
Bound States ◽  
Composite Particle ◽  
Composite Particles ◽  
Statistical Interpretation ◽  
Particle Spectrum ◽  
Nonlinear Spinor ◽  
Effective Interactions ◽  
Scattering States ◽  
Diagonal Part

Unified nonlinear spinor field models are selfregularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived. In this paper the dynamics of composite particles is discussed. The composite particles are defined to be eigensolutions of the diagonal part of the energy representation. Corresponding calculations are in preparation, but in the present paper a suitable composite particle spectrum is assumed. It consists of preon-antipreon boson states and threepreon- fermion states with corresponding antifermions and contains bound states as well as preon scattering states. The state functional is expanded in terms of these composite particle states with inclusion of preon scattering states. The transformation of the functional energy representation of the spinor field into composite particle functional operators produces a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. This representation is valid as long as the processes are assumed to be below the energetic threshold for preon production or preon break-up reactions, respectively. From this it can be concluded that below the threshold the effective interactions of composite particles in a unified spinor field model lead to phenomenological coupling theories which depend in their properties on the bound state spectrum of the self-regularizing spinor theory.

THE ANALOGUE OF THE AHARONOV–BOHM EFFECT FOR BOUND STATES FOR NEUTRAL PARTICLES

2011 ◽  
Vol 26 (18) ◽  
pp. 1331-1341 ◽  
Author(s):  
KNUT BAKKE ◽  
C. FURTADO
Keyword(s):  
Bound States ◽  
Neutral Particle ◽  
Energy Levels ◽  
Quantum Ring ◽  
Persistent Currents ◽  
One Dimensional ◽  
Neutral Particles ◽  
Quantum Flux ◽  
Bohm Effect ◽  
Aharonov Bohm

We study the analogue of the Aharonov–Bohm effect for bound states for a neutral particle with a permanent magnetic dipole moment interacting with an external field. We consider a neutral particle confined to moving between two coaxial cylinders and show the dependence of the energy levels on the Aharonov-Casher quantum flux. Moreover, we show that the same flux dependence of the bound states can be found when the neutral particle is confined to a one-dimensional quantum ring and a quantum dot, and we also calculate the persistent currents in each case.

Integrable and chaotic motions of four vortices II. Collision dynamics of vortex pairs

1988 ◽  
Vol 326 (1593) ◽  
pp. 655-696 ◽  
Keyword(s):  
Bound States ◽  
Degrees Of Freedom ◽  
Complex Structure ◽  
Physical Space ◽  
Vantage Point ◽  
Collision Dynamics ◽  
Chaotic Motions ◽  
Vortex Pairs ◽  
Scattering States ◽  
Space Mechanisms

The interaction of two vortex pairs is investigated analytically and by numerical experiments from the vantage point of dynamical-systems theory. Vortex pairs can escape to infinity, so the phase space of this system is unbounded in contrast to that of four identical vortices investigated previously. Chaotic motion is nevertheless possible both for ‘bound states’ of the system and for ‘scattering states’. For the bound states standard Poincare section techniques suffice. For scattering states chaos appears as complex structure in the numerically generated plot of scattering angle against impact parameter. Interpretations of physical space mechanisms leading to chaos are given. Analytical characterizations of the system include a formal reduction to two degrees of freedom by canonical transformations and an identification and discussion of integrable cases of which one is apparently new.

THE RELATIVISTIC BOUND AND SCATTERING STATES OF THE ECKART POTENTIAL WITH A PROPER NEW APPROXIMATE SCHEME FOR THE CENTRIFUGAL TERM

2009 ◽  
Vol 24 (01) ◽  
pp. 161-172 ◽  
Author(s):  
GAO-FENG WEI ◽  
SHI-HAI DONG ◽  
V. B. BEZERRA
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Scattering Amplitude ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Scattering States ◽  
Special Cases ◽  
Scattering State ◽  
Klein Gordon ◽  
Klein Gordon Equation

The approximately analytical bound and scattering state solutions of the arbitrary l wave Klein–Gordon equation for mixed Eckart potentials are obtained through a proper new approximation to the centrifugal term. The normalized analytical radial wave functions of the l wave Klein–Gordon equation with the mixed Eckart potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states reduce to those of the bound states at the poles of the scattering amplitude. Two special cases — for the s wave and for l = 0 and β = 0 — are also studied, briefly.

scholarly journals Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Soner Alpdoğan ◽  
Ali Havare
Keyword(s):  
Bound States ◽  
Dirac Particle ◽  
Saxon Potential ◽  
One Dimensional ◽  
Transmission And Reflection Coefficients ◽  
Scattering States ◽  
Transmission Resonances ◽  
The One ◽  
Dependent Mass ◽  
Position Dependent Mass

The one-dimensional Dirac equation with position dependent mass in the generalized asymmetric Woods-Saxon potential is solved in terms of the hypergeometric functions. The transmission and reflection coefficients are obtained by considering the one-dimensional electric current density for the Dirac particle and the equation describing the bound states is found by utilizing the continuity conditions of the obtained wave function. Also, by using the generalized asymmetric Woods-Saxon potential solutions, the scattering states are found out without making calculation for the Woods-Saxon, Hulthen, cusp potentials, and so forth, which are derived from the generalized asymmetric Woods-Saxon potential and the conditions describing transmission resonances and supercriticality are achieved. At the same time, the data obtained in this work are compared with the results achieved in earlier studies and are observed to be consistent.

scholarly journals Fingerprints of Majorana Bound States in Aharonov-Bohm Geometry

2016 ◽  
Vol 116 (16) ◽  
Author(s):  
Krashna Mohan Tripathi ◽  
Sourin Das ◽  
Sumathi Rao
Keyword(s):  
Bound States ◽  
Majorana Bound States ◽  
Aharonov Bohm
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