Related papers: Dirac Hamiltonian in a supersymmetric framework
Among the list of one dimensional solvable Hamiltonians, we find the Hamiltonian with the Rosen--Morse II potential. The first objective is to analyze the scattering matrix corresponding to this potential. We show that it includes a series…
The structure of the Dirac Hamiltonian in 3+1 dimensions is shown to emerge in a semi-classical approximation from a abstract spectral triple construction. The spectral triple is constructed over an algebra of holonomy loops, corresponding…
The simplest purely imaginary and piecewise constant $\cal PT$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete.…
We systematically formulate a hierarchy of isospectral Hamiltonians in one-dimensional supersymmetric quantum mechanics on an interval and on a circle, in which two successive Hamiltonians form N=2 supersymmetry. We find that boundary…
We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudosupersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the…
We study the Nonlinear (Polynomial, N-fold,...) Supersymmetry algebra in one-dimensional QM. Its structure is determined by the type of conjugation operation (Hermitian conjugation or transposition) and described with the help of the…
The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to…
The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…
We study certain new models of supersymmetric quantum mechanics. The explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonians and supercharges is given. It is shown that the Hamiltonian…
In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…
We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but an U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in…
A class of non-Hermitian quadratic su(2) Hamiltonians having an anti-linear symmetry is constructed. This is achieved by analysing the possible symmetries of such systems in terms of automorphisms of the algebra. In fact, different…
In the 70's Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and…
We study the Dirac-Kepler problem plus a Coulomb-type scalar potential by generalizing the Lippmann-Johnson operator to D spatial dimensions. From this operator, we construct the supersymmetric generators to obtain the energy spectrum for…
Interpolation of two adjacent Hamiltonians in SUSY quantum mechanics $H_s=(1-s)A^{\dagger}A + sAA^{\dagger}$, $0\le s\le 1$ is discussed together with related operators. For a wide variety of shape-invariant degree one quantum mechanics and…
It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian…
We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy…
We discuss the Dirac oscillator in $(1+1)$ and $(2+1)$ dimensions and generalize it in the spirit of the isotonic oscillator using supersymmetric quantum mechanics. In $(1+1)$ dimensions, the Dirac oscillator returns to the quantum harmonic…
The one-particle three-dimensional Dirac equation with spherical symmetry is solved for the Hulthen potential. The s-wave relativistic energy spectrum and two-component spinor wavefunctions are obtained analytically. Conforming to the…
Higher dimensional super symmetry has been analyzed in terms of quaternion variables and the theory of quaternion harmonic oscillator has been analyzed. Supersymmertization of quaternion Dirac equation has been developed for…