共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper consider the Darboux transform for the Dirac equation with a pseudoscalar-type potential. Formulas for the potential difference and for the solutions of the transformed equation are derived. The relationship between the Darboux transforms for Dirac and Schrödinger equations is analyzed. New potentials with the spectrum of a relativistic harmonic oscillator are obtained as examples. 相似文献
2.
Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials
We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity conditions are discussed. As an application, we consider a pseudoscalar Dirac potential related to the Schrödinger model for the rationally extended radial oscillator. The pseudoscalar partner potentials are constructed under the first- and second-order Darboux transformations. 相似文献
3.
A. A. Suzko 《Physics of Atomic Nuclei》2002,65(8):1553-1559
Darboux transformations and a factorization procedure are presented for a system of coupled finite-difference Schrödinger equations. The conformity between generalized Darboux transformations and the factorization method is established. Factorization chains and consequences of Darboux transformations are obtained for a system of coupled discrete Schrödinger equations. The proposed approach permits constructing a new series of potential matrices with known spectral characteristics for which coupled-channel discrete Schrödinger equations have exact solutions. 相似文献
4.
Axel Schulze-Halberg 《Central European Journal of Physics》2008,6(3):654-661
We construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy. 相似文献
5.
The Fokker–Planck equation associated with the two-dimensional stationary Schrödinger equation has the conservation law form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is considered. As the potential variable is a nonlocal variable for the Schrödinger equation that provides the nonlocal Darboux transformation for the Schrödinger equation. This nonlocal transformation is applied for obtaining of the exactly solvable two-dimensional stationary Schrödinger equations. The examples of exactly solvable two-dimensional stationary Schrödinger operators with smooth potentials decaying at infinity are obtained. 相似文献
6.
E. O. Pozdeeva 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2009,3(2):284-288
The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nuclear and Schwinger interactions of neutral particles with lattice sites during their channeling in the nonmagnetic crystal. The family of exactly solvable interaction Hamiltonians of a Schwinger type is obtained by means of the Darboux transformation chain. The analytic structure of the Lyapunov function of periodic continuation for each of the Hamiltonians of the family is considered. 相似文献
7.
In the present paper we solve the Dirac equation with Davidson potential by Nikiforov-Uvarov method. The Dirac Hamiltonian
contains a scalar S and a vector V Davidson potentials. With equal scalar and vector potential, analytical solutions for bound states of the corresponding Dirac
equations are found. 相似文献
8.
9.
Approximate analytical solutions of the Dirac equation are obtained for the Yukawa potential plus a tensor interaction with any κ-value for the cases having the Dirac equation pseudospin and spin symmetry. The potential describing tensor interaction has a Yukawa-like form. Closed forms of the energy eigenvalue equations and the spinor wave functions are computed by using the Nikiforov–Uvarov method. It is observed that the energy eigenvalue equations are consistent with the ones obtained before. Our numerical results are also listed to see the effect of the tensor interaction on the bound states. 相似文献
10.
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples. 相似文献
11.
The shifted-l expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or kvector potentials. A parameter λ = 0, l is introduced in such a way that one can obtain the Klein-Gordon (KG) bound states from Dirac bound states. The 4-vector Coulomb, the scalar linear, and the equally mixed scalar and 4-vector power-law potentials are used in KG and Dirac equations. Exact numerical results are obtained for the Cvector Coulomb potential in both KG and Dirac equations. Highly accurate and fast converging results are obtained for the scalar linear and the equally mixed scalar and 4-vector power-law potentials. 相似文献
12.
The equations for the general Darboux–Halphen system obtained as a reduction of the self-dual Yang–Mills can be transformed to a third-order system which resembles the classical Darboux–Halphen system with a common additive terms. It is shown that the transformed system can be further reduced to a constrained non-autonomous, non-homogeneous dynamical system. This dynamical system becomes homogeneous for the classical Darboux–Halphen case, and was studied in the context of self-dual Einstein's equations for Bianchi IX metrics. A Lax pair and Hamiltonian for this reduced system is derived and the solutions for the system are prescribed in terms of hypergeometric functions. 相似文献
13.
Axel Schulze-Halberg 《Physics letters. A》2011,375(25):2513-2518
We construct a new type of first-order Darboux transformations for the stationary Schrödinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schrödinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) [16] as a special case. 相似文献
14.
Jouko Mickelsson 《Letters in Mathematical Physics》1982,6(3):221-230
It is shown that the Dirac equation can be written in a form similar to Maxwell equations, where the Maxwell tensor is written
as a bilinear expression of the Dirac field and the current is a simple function of the external potential and the Dirac field.
Similarly, the Maxwell equations can be written as a self-coupled Dirac equation where the potential is a simple function
of the Dirac field itself. It is illustrated by examples how the new formalism helps to find solutions of the coupled field
equations. 相似文献
15.
16.
We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. 相似文献
17.
Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initial-boundary problems are formulated. 相似文献
18.
We develop the Darboux procedure for the case of the two‐level system. In particular, it is demonstrated that one can construct the Darboux intertwining operator that does not violate the specific structure of the equations of the two‐level system, transforming only one real potential into another real potential. We apply the obtained Darboux transformation to known exact solutions of the two‐level system. Thus, we find three classes of new solutions for the two‐level system and the corresponding new potentials that allow such solutions. 相似文献
19.
Based on the method oftransformation operators, the Darboux transformation operator has been constructed for the one-dimensional stationary Dirac equation. The properties of this operator have been studied. As an application, exactly solvable transparent potentials and potentials with the spectrum of a relativistic harmonic oscillator have been obtained. 相似文献
20.
Kostyantyn Zheltukhin Natalya Zheltukhina 《Journal of Nonlinear Mathematical Physics》2018,25(1):166-177
We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable. 相似文献