arXiv subjects

S. B. Faruque

Publications and source records attributed to S. B. Faruque.

5 recordsLinked to original sources

arXiv2019

Localized states of Dirac equation

In this paper, we introduce an extension of the Dirac equation, very similar to Dirac oscillator, that gives stationary localized wave packets as eigenstates of the equation. The extension to the Dirac equation is achieved through the replacement of the momentum operator by a PT-symmetric generalized momentum operator. In the 1D case, the solutions represent bound particles carrying spin having continuous energy spectrum, where the envelope parameter defines the width of the packet without affecting the dispersion relation of the original Dirac equation. In the 2D case, the solutions are localized wave packets and are eigenstates of the third component of total angular momentum and involve Bessel functions of integral order. In the 3D case, the solutions are localized spherical wave packets with definite total angular momentum.

quant-ph↗

arXiv2017

A new approach to Gravity

Beginning with a decomposition of the Newtonian field of gravity, I show that four classical color fields can be associated with the gravitational field. The meaning of color here is that these fields do not add up to yield the Newtonian gravitational field, but the forces and potential energies associated with them add up to yield the Newtonian force and potential energy, respectively. These four color fields can have associated magnetic fields as in linearized gravity. Thus we envisage a theory where four sets of Maxwellian equations would prevail. A quantum gravity theory with four spin 1 fields can thus be envisaged.

physics.gen-ph↗

arXiv2016

A short note on minimal length

After revival of the concept of minimal length, many investigations have been devoted, in literature, to estimate upper-bound on minimal length for systems like hydrogen atom, deuteron etc. We report here a possible origin of minimal length for atomic and nuclear systems which is connected with the fundamental interaction strength and the Compton wavelength. The formula we appear at is numerically close to the upper-bounds found in literature.

quant-ph↗

arXiv2015

Novel energy level structure of Dirac oscillator in magnetic field

We have presented an elegant high energy quantum problem, namely, the full Dirac oscillator under axial magnetic field with its full solution. We have found the energy spectrum which is rich and at the same time has a novel structure. The quantized energy levels show coupling of the oscillator frequency with the Larmor frequency in the 2D surface where the electrons under consideration follow a 2D oscillator. The axis in which magnetic field is pointed, the electrons follow a 1D oscillator. There is also coupling between spin and orbital motion and also a coupling between a resultant effect of orbital and spin motion with Larmor precession.

quant-ph↗

arXiv2015

On the gravitomagnetic clock effect in quantum mechanics

In this article, we discuss how to carryover gravitomagnetic clock effect from classical general relativity to quantum theory and how to calculate this effect in quantum mechanics. Our calculation is valid for semi-classical regime and can be considered as the first step towards a complete gravitomagnetic quantum theory. We also show the analogy between energy levels that corresponds to the clock effect. In fact, it is argued that in quantum mechanics clock effect arises as energy level splitting in gravitomagnetic field.

quant-ph↗