Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fortschritte der Physik

Coherent states for hydrogen‐like atom in the presence of Aharonov‐Bohm effect

G. E. Drăgănescu, N.M. Avram

Published Feb 26, 2003• 2 citations
Publisher

Abstract

Abstract For a hydrogenlike atom introduced in an Aharonov‐Bohm potential due a infinite solenoid it was established different operators corresponding to different representations of the system. For this system we studied the the displacement coherent states and harmonic oscillatorlike coherent states. The average values of some observables in different coherent states have been done.

DOI
10.1002/prop.200310010

Related papers

Radial coherent states for Dirac hydrogen-like atom

G. E. Drăgănescu, ANTONINO MESSINA, Anna Napoli

In this paper we use an su (2) representation of the radial eigenfunction of the Dirac hydrogen-like atom and we build the Glauber coherent states and the displacement operator coherent states. We also calculate the average values of some observables corresponding to these states.

Journal of Optics B Quantum and Semiclassical Optics•Jun 10, 2002•7 citations

A time-dependent 2D harmonic oscillator in the presence of the Aharonov–Bohm effect with a time-dependent flux radius

Mustapha Maamache, Nadir Chaabi, Y. Saadi

The quantum states of the 2D time-dependent harmonic oscillator with the Aharonov–Bohm (AB) effect are investigated by employing the invariant operator method and the unitary transformation approach. The time-dependent radius case of a solenoid is treated. The qualitative properties of the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation, i.e. C>0, C=0 and C 0) or continuous (C≤0). The time-dependent cross section for a free particle scattered by the AB potential is obtained.

Physica Scripta•Dec 19, 2008•1 citation

Coherent states of non-relativistic electron in the magnetic–solenoid field

Vladislav G. Bagrov, Sergei P. Gavrilov, Dmitri M Gitman +1 more

In the present work we construct coherent states in the magnetic–solenoid field, which is a superposition of the Aharonov–Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kinds of coherent states, those which correspond to classical trajectories which embrace the solenoid and those which do not. The constructed coherent states reproduce exactly classical trajectories, maintain their form under the time evolution and form a complete set of functions, which can be useful in semiclassical calculations. In the absence of the solenoid field these states are reduced to the well known in the case of uniform magnetic field Malkin–Man'ko coherent states.

arXiv:1002.2256•Journal of Physics A Mathematical and Theoretical•Aug 12, 2010•7 citations

Aharonov-Bohm effect without contact with the solenoid

César R. de Oliveira, Renan G. Romano

We add a scalar potential to the 2D Aharonov-Bohm (AB) model which properly diverges both at the solenoid border and at infinity so that the resulting operator is essentially self-adjoint and has a discrete spectrum; the former property is interpreted as no contact of the particle with the solenoid border since there is no need of boundary conditions. We study gauge transformations to get the usual periodic behavior of the AB properties as a function of the magnetic flux. The presence of the AB effect is proven through the ground state energy, which is shown to be smooth in case it is simple and with a nonzero derivative if the ground state is real valued; such properties are verified in the case of circular solenoids, for which it is shown to be a nonconstant periodic function with a minimum at integer and a maximum at half-integer circulations (at half-integer circulations, it is doubly degenerated).

arXiv:1711.06525•Journal of Mathematical Physics•Oct 1, 2017•4 citations

Coherent and semiclassical states in a magnetic field in the presence of the Aharonov–Bohm solenoid

V G Bagrov, Sergei P. Gavrilov, D M Gitman +1 more

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy -plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

arXiv:1008.1768•Journal of Physics A Mathematical and Theoretical•Jan 4, 2011•24 citations

Complemetarity of Phases in Aharonov-Bohm Solenoid Effect

Y. Ben-Aryeh

In the present Note it is suggested that there should be a certain complementarity of phases between Aharonov-Bohm (AB) solenoid phase calculation on one part of the system and a phase calculation about another part of the physical system. Assuming a unique value for the function of the total system, after a complete circulation of the electron around the solenoid, the sum of these two phase changes should vanish. Such assumption leads to a compatibility relation between our previous calculations for the AB solenoid phase effect and that of the original calculation by AB.

arXiv:1112.4958•Dec 21, 2011•1 citation
Abstract For a hydrogenlike atom introduced in an Aharonov‐Bohm potential due a infinite solenoid it was established different operators corresponding to different representations of the system. For this system we studied the the displacement coherent states and harmonic oscillatorlike coherent states. The average values of some observables in different coherent states have been done.
The quantum states of the 2D time-dependent harmonic oscillator with the Aharonov–Bohm (AB) effect are investigated by employing the invariant operator method and the unitary transformation approach. The time-dependent radius case of a solenoid is treated. The qualitative properties of the invariant operator spectrum are described separately for the different values of the parameter C appearing in the nonlinear auxiliary equation, i.e. C>0, C=0 and C 0) or continuous (C≤0). The time-dependent cross section for a free particle scattered by the AB potential is obtained.
In the present work we construct coherent states in the magnetic–solenoid field, which is a superposition of the Aharonov–Bohm field and a collinear uniform magnetic field. In the problem under consideration there are two kinds of coherent states, those which correspond to classical trajectories which embrace the solenoid and those which do not. The constructed coherent states reproduce exactly classical trajectories, maintain their form under the time evolution and form a complete set of functions, which can be useful in semiclassical calculations. In the absence of the solenoid field these states are reduced to the well known in the case of uniform magnetic field Malkin–Man'ko coherent states.
We add a scalar potential to the 2D Aharonov-Bohm (AB) model which properly diverges both at the solenoid border and at infinity so that the resulting operator is essentially self-adjoint and has a discrete spectrum; the former property is interpreted as no contact of the particle with the solenoid border since there is no need of boundary conditions. We study gauge transformations to get the usual periodic behavior of the AB properties as a function of the magnetic flux. The presence of the AB effect is proven through the ground state energy, which is shown to be smooth in case it is simple and with a nonzero derivative if the ground state is real valued; such properties are verified in the case of circular solenoids, for which it is shown to be a nonconstant periodic function with a minimum at integer and a maximum at half-integer circulations (at half-integer circulations, it is doubly degenerated).
A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy -plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.
In the present Note it is suggested that there should be a certain complementarity of phases between Aharonov-Bohm (AB) solenoid phase calculation on one part of the system and a phase calculation about another part of the physical system. Assuming a unique value for the function of the total system, after a complete circulation of the electron around the solenoid, the sum of these two phase changes should vanish. Such assumption leads to a compatibility relation between our previous calculations for the AB solenoid phase effect and that of the original calculation by AB.