Related papers: Coherent Schwinger Interaction from Darboux Transf…
We consider the Dirac equation written in polar form, without any external potential but equipped with a non-zero tensorial connection, and we find a new type of solution that is localized around the origin with a decreasing exponential…
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 paper we study a family of one-dimensional stationary cubic nonlinear Schr\"odinger (NLS) equations with periodic potentials and linear part displaying Dirac points in the dispersion relation. By introducing a suitable periodic…
Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux…
It is shown that in case of central potentials, both the fourth component of Lorentz vector as well as Lorentz scalar in the Dirac Hamiltonian, owing to the conserved Dirac spin-orbital matrix, there arises Wittens N=2 superalgebra. The…
The problem of a fermion subject to a general scalar potential in a two-dimensional world is mapped into a Sturm-Liouville problem for nonzero eigenenergies. The searching for possible bounded solutions is done in the circumstance of…
By combining stability analysis of scalar field theories with the Darboux transformation technique, we create models featuring kink-like solutions whose quantum perturbations are all bounded. On the one hand, the stability analysis relates…
The dynamics of relativistic (scalar and vector) bosons through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrodinger…
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…
In this work, we investigate the dynamical breakdown of Lorentz symmetry in 4 dimensions by the condensation of a fermionic field described by a Dirac Lagrangian with a four-fermion interaction. Using the Keldysh formalism we show that the…
The article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the class of nonlinear Schr\"odinger equations. The well-known…
An effective approach is presented to produce Schrodinger-like equation for the spinor components from Dirac equation. Considering electrostatic potential as a constant value yields a second-order differential equation that is comparable…
We introduce GBDT version of Darboux transformation for symplectic and Hamiltonian systems as well as for Shin-Zettl systems and Sturm-Liouville equations. These are the first results on Darboux transformation for general-type Hamiltonian…
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
In [1], a generalized type of Darboux transformations defined in terms of a twisted derivation was constructed in a unified form. Such twisted derivations include regular derivations, difference operators, superderivatives and…
In lattice QCD, a confining potential for a static quark-antiquark pair can be computed with the Wilson loop technique. This potential, dominated by a linear potential at moderate distances, is consistent with the confinement with a flux…
Chains of Darboux transformations for the matrix Schroedinger equation are considered. Matrix generalization of the well-known for the scalar equation Crum-Krein formulas for the resulting action of such chains is given.
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in beta and a steep harmonic oscillator in gamma, centered around gamma=30 degrees, is developed. Analytical expressions for spectra and…
Positive definiteness of the quadratic part of the action of the Hawking-Turok instanton is investigated. The Euclidean quadratic action for scalar perturbations is expressed in terms of a single gauge invariant quantity $q$. The mode…