相关论文: Solving simultaneously Dirac and Ricatti equations

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical…

We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show…

The factorization method was introduced by Schroedinger in 1940. Its use in bound-state problems is widely known, including in supersymmetric quantum mechanics; one can create a factorization chain, which simultaneously solves a sequence of…

The time-dependent Dirac equation is solved using the three-dimensional Finite Difference-Time Domain (FDTD) method. The dynamics of the electron wave packet in a scalar potential is studied in the arrangements associated with the Klein…

We apply the technique of standard supersymmetric factorization for any q factor ordering in the Wheeler-DeWitt (WDW) equation for barotropic Friedmann-Robertson-Walker (FRW) minisuperspace model, including the cosmological term. The…

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase…

We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…

We employ the techniques introduced in the companion papers to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D+1 > 2 with compact gauge group. The technique that accomplishes that…

A family of cosmological solutions with $(n+1)$ Ricci-flat spaces in the theory with several scalar fields and multiple exponential potential is obtained when coupling vectors in exponents obey certain relations. Two subclasses of solutions…

We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient…

In this work we exploit Dirac's Constraint Analysis (DCA) in Hamiltonian formalism to study different types of Superconducting Quantum Circuits (SQC) in a {\it{unified}} way. The Lagrangian of a SQC reveals the constraints, that are…

We investigate the planar Dirac equation with the most general time-independent contact (singular) potential supported on a circumference. Taking advantage of the radial symmetry, the problem is effectively reduced to a one-dimensional one…

In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac…

We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of…

The factorizations using the general Riccati solution constructed from a given particular solution by means of the Bernoulli ansatz initiated in 1984 by Mielnik and Fernandez C. for the cases of the quantum harmonic oscillator and the…

The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…

Using the method of $su(1,1)$ spectrum generating algebra, we analyze one dimensional Schroedinger equation with potential in the form ${C\over{x^2} + {D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a group…

Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in…

In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which…

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…