Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun's differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states.

show abstract

“…are the upper and lower spinor components of the Dirac wavefunctions, respectively [72,73]. Substituting it into Eq.…”

Section: The Spin Symmetrymentioning

confidence: 99%

Relativistic Killingbeck energy states under external magnetic fields

2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…We refer the readers to Ref. [21,22,23] for more details and general examples involving the application of formula method. From equation 4, we have…”

Section: φ ′′ ( ) + ( 1 − 2 )∕( −mentioning

confidence: 99%

Enhancing the energy spectrum of graphene quantum dot with external magnetic and Aharonov-Bohm flux fields

Serrano

Avalos

Rivas

et al. 2019

Heliyon

View full text Add to dashboard Cite

In this paper, we have to apply the Dirac-Weyl equation to find the analytical energy eigenvalues of the graphene quantum dot interacting in the presence of AB-flux field and external magnetic field. We find that the energy eigenvalue of the graphene quantum dot decreases with both magnetic and AB-flux field but the effect of AB-flux field is more dominant. By ameliorating the intensity of the AB-flux field and keeping the magnetic field constant, the quantum-dot states entangled to produce Landau Levels. We show that besides using the graphene sheet and external magnetic field, the Aharonov-Bohm AB-flux field could as well be used to manipulate the carriers state energies in graphene.

show abstract

“…In such scenarios, the Heisenberg uncertainty relation necessarily modifies to a generalized version to the so-called generalized uncertainty principle (GUP). Over last two decades, it is known that within this framework, in particular, where the space-time commutation relation involves higher powers of momenta, explicitly leads to the existence of nonzero minimal uncertainty in position coordinate, which is familiar as the minimal length in the literature [88,[93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108]. An intimate connection between the gravitation and the existence of the fundamental length scale was proposed in [109].…”

Section: A Noncommutative Quantum Mechanicsmentioning

confidence: 99%

Coherent States and Their Applications

2018

Springer Proceedings in Physics

View full text Add to dashboard Cite

It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as "coherent states" today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community.

show abstract

Massive fermions interacting via a harmonic oscillator in the presence of a minimal length uncertainty relation

Cited by 11 publications

References 42 publications

Relativistic Killingbeck energy states under external magnetic fields

Relativistic Killingbeck energy states under external magnetic fields

Enhancing the energy spectrum of graphene quantum dot with external magnetic and Aharonov-Bohm flux fields

Coherent States and Their Applications

Contact Info

Product

Resources

About