Related papers: Levinson's Theorem for Dirac Equation
We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within the Anti-Snyder modified uncertainty relation characterized by a momentum cut-off ($p\leq p_{\text{max}}=1/ \sqrt{\beta}$). In…
We review the standards of relativistic quantum mechanics such as the Dirac equation under the concept of negative masses. We show that negative energies are acceptable provided the masses are simultaneously negative. Negative energy and…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
We consider the consistent deformation of the relativistic quantum mechanics introducing the noncommutativity of the space-time and preserving the Lorentz symmetry. The relativistic wave equation describing the spinning particle on…
In this paper, we revisit the connection between the Riemann-Roch theorem and the zero energy solutions of the two-dimensional Dirac equation in the presence of a delta-function like magnetic field. Our main result is the resolution of a…
The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of…
We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.
We figure out the famous Klein's paradox arising from the reflection problem when a Dirac particle encounters a step potential with infinite width. The key is to piecewise solve Dirac equation in such a way that in the region where the…
The relativistic theory of the Dirac fermions moving on cylinders in external Aharonov-Bohm field is built starting with a suitably restricted Dirac equation whose spin degrees of freedom are not affected. The exact solutions of this…
Changes in the magnetic moment of an electron near a dielectric or conducting surface due to boundary-dependent radiative corrections are investigated. The electromagnetic field is quantized by normal mode expansion for a non-dispersive…
It was long believed that there is a zero-point energy in the form of h\omega/2 for massive particles, which is obtained from Schr\"odinger equation for the harmonic oscillator model. In this paper, it is shown, by the Dirac oscillator,…
Using the China unitary principle to test the Dirac theoryfor the hydrogen atomic spectrum shows that the standard Dirac function withthe Dirac energy levels is only one the formal solutions of theDirac-Coulomb equation, which conceals some…
In Dirac's hole theory the vacuum state is generally believed to be the state of minimum energy. However it has recently been shown that this is not the case. In [1] it was shown that energy can be extracted from the hole theory vacuum…
Using a generalized procedure for obtaining the equation of motion of a propagating fermionic particle, we examine previous claims for a lightlike preferred axis embedded in the framework of Lorentz-invariance violation with preserved…
We derive an exact solitary wave solution for the $\PTb$-symmetric nonlinear Dirac equation with a scalar-scalar interaction. We consider a power-law nonlinearity of the form $|\bar{\Psi}\,\Psi|^{k}\,\Psi$ for positive values of $k$. The…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
The thermodynamic equations of state for Majorana and Dirac fermions are quite different even in the limit of zero mass. The corresponding equations are derived from general principles, and then applied to neutrinos. The nature of the…
In this comment, we obtain the complete energy spectra for the paper by Sahan et al. [1], that is, the energy spectra dependent on two quantum numbers, namely, the radial quantum number (given by $n\geq 0$) and the angular quantum number…