Related papers: Levinson's Theorem for Dirac Equation
The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville…
In the case of the one-electron Dirac equation with a point nucleus the Virial Theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly $-1$, a ratio that can be an independent test of the accuracy of a…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
A quantum phase space version of the continuity equation for systems with internal degrees of freedom is derived. The $1$ -- D Dirac equation is introduced and its phase space counterpart is found. The phase space representation of free…
We consider the Dirac field in polar formulation, showing that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas, that when the limit of zero chiral angle is taken the theory…
It is proposed to make formulation of second quantizing a bosonic theory by generalizing the method of filling the Dirac negative energy sea for fermions. We interpret that the correct vacuum for the bosonic theory is obtained by adding…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
This paper is motivated by the recent paper M. Baldovin, S. Iubini, R. Livi and A. Vulpiani, Statistical mechanics of systems with negative temperature, arXiv:2103.12572. The authors suggest that negative absolute temperatures are…
The Dirac-Coulomb equation with positive-energy projection is solved using explicitly correlated Gaussian functions. The algorithm and computational procedure aims for a parts-per-billion convergence of the energy to provide a starting…
It was known that a free, nonrelativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current --- hence termed quantum backflow. Here, it is shown that more variations can be brought…
It is shown that in the two-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are…
Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be…
The Dirac equation is solved for two novel terms which describe the interaction energy between the half integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the…
In Dirac's hole theory the vacuum state is generally believed to be the state of minimum energy. It will be shown that this is not, in fact, the case and that there must exist states in hole theory with less energy than the vacuum state. It…
The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…
Dirac field theory is assumed to be gauge invariant. However it is well known that a calculation of the polarization tensor yields a non-gauge invariant result. The reason for this has been shown to be due to the fact that for Dirac theory…
Quantum dynamics of a Dirac particle in a 1D box with moving wall is studied. Dirac equation with time-dependent boundary condition is mapped onto that with static one, but with time-dependent mass. Exact analytical solution of such…
In this paper we consider torsion gravity in the case of the Dirac field, and by going into the rest frame we study what happens when a uniform precession as well as a phase are taken into account for the spinor field; we discuss how…
The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for…
We obtain the two-point Green's function for the relativistic Dirac-Oscillator problem. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and…