Related papers: Comment on "Position-dependent effective mass Dira…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
The modified Dirac equations for the massive particles with the replacement of the physical mass $m$ with the help of the relation $m\rightarrow m_1 + \gamma_5 m_2$ are investigated. It is shown that for a free fermion theory with a…
We present a large class of non-Hermitian non-PT-symmetric two-component Dirac Hamiltoninas with real energy spectra. These Hamiltonians are invariant under the combined action of "charge" conjugation (two-component transpose) and…
A realistic interpretation of Schroedinger and Dirac equations for density matrices is proposed, in which the difference between the position arguments of the density matrix is considered as an objective extra space dimension. "Particle"…
We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…
We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the…
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…
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type…
We consider $(2+1)$ dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states and the Dirac Hamiltonians are…
Parity-time ($\mathcal{PT}$) symmetry plays an important role both in non-Hermitian and topological systems. In non-Hermitian systems $\mathcal{PT}$ symmetry can lead to an entirely real energy spectrum, while in topological systems…
Two dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the…
This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…
Two dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parametrization, the Dirac operator on the sphere is presented and the system is given as…
We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
Despite its common use in quantum theory, the mathematical requirement of Dirac Hermiticity of a Hamiltonian is sufficient to guarantee the reality of energy eigenvalues but not necessary. By establishing three theorems, this paper gives…
I consider the longstanding issue of the hermiticity of the Dirac equation in curved spacetime. Instead of imposing hermiticity by adding ad hoc terms, I renormalize the field by a scaling function, which is related to the determinant of…
With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions…
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…