Related papers: Exact energy quantization condition for single Dir…
In quantum field theory there exist states for which the energy density is negative. It is important that these negative energy densities satisfy constraints, such as quantum inequalities, to minimize possible violations of causality, the…
We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar $S$ and vector $V$ confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has $V=\pm…
We study both one and two-phase minimisers of the Dirichlet-area energy $$E(v) = \int_{B_1} \vert\nabla v\vert^2 + Per(\{v>0\},B_1).$$ In the two-phase case, we show that the energies $$E_{\varepsilon}(v) = \int_{B_1}\vert\nabla v\vert^2 +…
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the…
We construct general solutions of the time-dependent Dirac equation in (1+1) dimensions with a Lorentz scalar potential, subject to the so-called Majorana condition, in the Majorana representation. In this situation, these solutions are…
Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic…
In this work, a spin $\frac 12$ relativistic particle described by a generalized potential containing both the Coulomb potential and a Lorentz scalar potential in Dirac equation is investigated in terms of the generalized ladder operators…
We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov-Shabat) operator on the real line with general analytic potential. We provide Bohr-Sommerfeld quantization conditions near energy levels where the potential exhibits…
We study a relativistic charged Dirac particle moving in a rotating magnetic field. By using a time-dependent unitary transformation, the Dirac equation with the time-dependent Hamiltonian can be reduced to a Dirac-like equation with a…
A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}= -\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by $V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocation method…
Fewster and Mistry have given an explicit, non-optimal quantum weak energy inequality that constrains the smeared energy density of Dirac fields in Minkowski spacetime. Here, their argument is adapted to the case of flat, two-dimensional…
It has been observed that a quantum mechanical theory need not to be Hermitian to have a real spectrum. In this paper we obtain the eigenvalues of a Dirac charged particle in a complex static and spherically symmetric potential.…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important…
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
In this article we present a study of the effects of hydrostatic pressure on the energy levels of a quantum dot with an electron. A quantum dot is modeled using an infinite potential well and a two-dimensional harmonic oscillator and solved…
The unitary transformation, which diagonalizes squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of diagonalized Hamiltonian, that describe the states with definite…
In this paper we consider a model of the Dirac vacuum in classical electromagnetic fields at positive temperature. We adopt the Pauli-Villars regularisation technique in order to properly define the free energy of the vacuum, extending the…
Since the structure of space-time at very short distances is believed to get modified possibly due to noncommutativity effects and as the Dirac Quantization Condition (DQC), $\mu e = \frac{N}{2}\hbar c$, probes the magnetic field point…
In this work, we propose a novel variational quantum approach for solving a class of nonlinear optimal control problems. Our approach integrates Dirac's canonical quantization of dynamical systems with the solution of the ground state of…