Related papers: A Master Equation Approach to the `3 + 1' Dirac Eq…
One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the…
We discuss the most general form of Dirac equation in the non$-$Riemannian spacetimes containing curvature, torsion and non$-$metricity. It includes all bases of the Clifford algebra $cl(1,3)$ within the spinor connection. We adopt two…
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
The Lagrangian approach of Dirac is presented in a complete form. This suggests to identify the Schr\"{o}dinger equation as the Euler-Lagrange equation rather than the Hamiltonian operator equation.
A version of the binary Darboux transformation is constructed for non-stationary Schroedinger equation in dimension $k+1$, where $k$ is the number of space variables, $k \geq 1$. This is an iterated GBDT version. New families of…
Spectrum of the Dirac Equation is obtained algebraically for arbitrary combination of Lorentz-scalar and Lorentz-vector Coulomb potentials using the Witten's Superalgebra approach. The result coincides with that, known from the explicit…
We find an exact solution to the Dirac equation in 1-1 dimensional space-time in the presence of a time-dependent potential which consists of a combination of electric, scalar, and pseudoscalar terms.
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We investigate the exact solution, perturbation theory and master equation of open system dynamics based on our serial studies on quantum mechanics in general quantum systems [An Min Wang, quant-ph/0611216 and quant-ph/0611217]. In a…
A three-dimensional Riccati differential equation of complex quaternion-valued functions is studied. Many properties similar to those of the ordinary differential Riccati equation such that linearization and Picard theorem are obtained. Lie…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
We show that the Dirac factorization method can be successfully employed to treat problems involving operators raised to a fractional power. The technique we adopt is based on an extension of the Pauli matrices and the properties of the…
We solve the Schwinger-Dyson equations for QED in 2+1 or 3+1 dimensions in the presence of a strong homogeneous external magnetic field. The magnetic field is assumed strong enough, so that the lowest Landau level approximation holds, but…
It is shown that the known method to solve the Dirac equation by means of the squaring method, when relying on the scalar function of the form \Phi = e^{-i\epsilon t} e^{ik_{1} x} e^{ik_{2} y} \sin (kz + \alpha) leads to a 4-dimensional…
The $k$-subset sum problem over finite fields is a classical NP-complete problem.Motivated by coding theory applications, a more complex problem is the higher $m$-th moment $k$-subset sum problem over finite fields. We show that there is a…
In this paper, we give two new generalizations of Clarkson-McCarthy with several operators, which depends on the unitary orbit technique developed by Bourin, Hadamard Three-lines Theorem and the duality argument developed by Ball, Carlen…
In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately…
The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and…
We present a 3+1 formulation of the effective field theory framework called the Standard-Model Extension in the gravitational sector. The explicit local Lorentz and diffeomorphism symmetry breaking assumption is adopted and we perform a…