Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSplitting the Dirac equation: the case of longitudinal potentials
221
0
0.0
(
0
)
Authors
Andrzej Okninski
Ask ChatGPT about the research
No Arabic abstract
Recently, we have demonstrated that some subsolutions of the free Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with some built-in projection operators. In the present paper we study the Dirac equation in the interacting case. It is demonstrated that the Dirac equation in longitudinal external fields can be also splitted into two covariant subequations.
rate research
Read More
Dirac equation is solved for some exponential potentials, hypergeometric-type potential, generalized Morse potential and Poschl-Teller potential with any spin-orbit quantum number $kappa$ in the case of spin and pseudospin symmetry, respectively. We have approximated for non s-waves the centrifugal term by an exponential form. The energy eigenvalue equations, and the corresponding wave functions are obtained by using the generalization of the Nikiforov-Uvarov method.
A derivation of the Dirac equation in `3+1 dimensions is presented based on a master equation approach originally developed for the `1+1 problem by McKeon and Ord. The method of derivation presented here suggests a mechanism by which the work of Knuth and Bahrenyi on causal sets may be extended to a derivation of the Dirac equation in the context of an inference problem.
The tt* equation that we will study here is classed as case 4a by Guest et al. in their series of papers Isomomodromy aspects of the tt* equations of Cecotti and Vafa. In their comprehensive works, Guest et al. give a lot of beautiful formulas on and finally achieve a complete picture of asymptotic data, Stokes data and holomorphic data. But, some of their formulas are complicated, lacking of intuitional explanation or other relevant results that could directly support them. In this paper, we will first verify numerically their formulas among the asymptotic data and Stokes data. Then, we will enlarge the solution class assumed by Guest et al. from the Stoke data side. Based on the numerical results, we put forward a conjecture on the enlarged class of solutions. At last, some trial to enlarge the solution class from the asymptotic data are done. It is the truncation structure of the tt* equation that enables us to do those numerical studies with a satisfactory high precision.
We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
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 considered. Algebraic method is used in the calculations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
