Related papers: Overcritical PT-symmetric square well potential in…
The Parity-Time ($\mathcal{PT}$) symmetric potentials are derived by non-Hermitian supersymmetric quantum mechanics for square well and barrier. These $\mathcal{PT}$-supersymmetric square well and barrier. The partners have complex…
We obtain an exact solution of the 1D Dirac equation for a square well potential of depth greater then twice the particle's mass. The energy spectrum formula in the Klein zone is surprisingly very simple and independent of the depth of the…
A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being instead delta function normalized. This lack of square…
A particle moving on a circle in a purely imaginary one-step potential is studied in both the exact and broken $PT$-symmetric regime.
An elementary treatment of the Dirac Equation in the presence of a three-dimensional spherically symmetric $\delta (r-r_0)$-potential is presented. We show how to handle the matching conditions in the configuration space, and discuss the…
Discrete PT-symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain…
The construction of Dirac delta type potentials has been achieved with the use of the theory of self adjoint extensions of non-self adjoint formally Hermitian (symmetric) operators. The application of this formalism to investigate the…
In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}2$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in $s_{1/2}$ states (with $\kappa=-1$) and…
In a box of size $L$, a spatially antisymmetric square-well potential of a purely imaginary strength ${\rm i}g$ and size $l < L$ is interpreted as an initial element of the SUSY hierarchy of solvable Hamiltonians, the energies of which are…
Coupled pair of PT-symmetric square wells is studied as a prototype of a quantum system characterized by two manifestly non-Hermitian commuting observables. We demonstrate that there exists a domain of couplings where both the respective…
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…
New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values…
The Dirac equation in (1+1) dimensions with a non-local PT-symmetric potential of separable type is studied by means of the Green function method: properties of bound and scattering states are derived in full detail and numerical results…
The path is explored between one-dimensional scattering through Dirac-$\delta$ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two $\delta$'s are…
An elementary treatment of the Dirac equation in the presence of a three dimensional spherically symmetric delta potential is presented. We show how to calculate the cross section using the relativistic wave expansion method for a one delta…
The combination of gain and loss in optical systems that respect parity-time (PT)-symmetry has pointed recently to a variety of novel optical phenomena and possibilities. Many of them can be realized by combining the PT-symmetry concepts…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
We study an anti-symmetric (square) well and barrier potential of depth/height $(V_0)$ placed between two rigid walls. Unlike the usual double-well, here the closely lying sub-barrier doublets need not be the lowest ones in the spectrum.…
The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…