共查询到20条相似文献,搜索用时 13 毫秒
1.
The Darboux Transformation for the One-Dimensional Stationary Dirac Equation with a Scalar Potential
This paper deals with the Darboux transformation for the Dirac equation with a scalar-type potential. Formulas are derived for the potential difference and for the solutions of the transformed equations. The relationship between the Darboux transforms for Dirac and Schrödinger equations is analyzed. New transparent potentials and a potential with a Coulomb asymptotics are obtained as examples. 相似文献
2.
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
3.
The method of differential transformation operators is applied to the Dirac equation with the generalized form of the time-dependent potential. It is demonstrated that the transformation operator and the transformed potential are solutions of the initial equation. It is established that under certain conditions, an integral expression can be retrieved for the transformed potential. Examples of new potentials expressed through elementary functions are presented for which the Dirac equation can be solved exactly.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 34–41, April, 2005. 相似文献
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We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable forthe case with time-independence mass. 相似文献
6.
YANGJin XIANGAn-Ping YUWan-Lun 《理论物理通讯》2003,40(3):283-284
We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable for the case with time-independence mass. 相似文献
7.
An approximation method, namely, the Extended Wronskian
Determinant Approach, is suggested to study the one-dimensional
Dirac equation. An integral equation, which can be solved by
iterative procedure to find the wave functions, is established. We
employ this approach to study the one-dimensional Dirac equation
with one-well potential, and give the energy levels and wave
functions up to the first order iterative approximation. For
double-well potential, the energy levels up to the first order
approximation are given. 相似文献
8.
We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem. The explicit solution of Tzitzeica equation is obtained. 相似文献
9.
《理论物理通讯》2015,(11)
A coupled system known as tie Drinfel'd-Sokolov-Wilson equation is reexamined.With the help of a Lax operator of fourth order,its proper Darboux transformation is constructed.Also,a nonlinear superposition formula is worked out for the associated Backlund transformation and some solutions are calculated. 相似文献
10.
A coupled system known as the Drinfel'd-Sokolov-Wilson equation is reexamined. With the help of a Lax operator of fourth order, its proper Darboux transformation is constructed. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation and some solutions are calculated. 相似文献
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12.
Dierck-Ekkehard Liebscher 《Annalen der Physik》1985,497(1):35-40
We discuss the problem of the derivation and the interpretation of metric tensors and generalized equations of motion for test particles from quasilinear spinor equations. 相似文献
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We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator \({\int\limits_{0} ^{\infty}{\rm e}^{iH_{0}t}\zeta(\frac{\vert x\vert }{R}) {\rm e}^{-iH_{0}t}{\rm d}t}\), as \({R \rightarrow \infty}\), is presented. Here, H0 is the free Dirac operator and \({\zeta\left(t\right)}\) is such that \({\zeta\left(t\right) = 1}\) for \({0 \leq t \leq 1}\) and \({\zeta\left(t\right) = 0}\) for \({t > 1}\). This approach allows us to obtain the time delay operator \({\delta \mathcal{T}\left(f\right)}\) for initial states f in \({\mathcal{H} _{2}^{3/2+\varepsilon}(\mathbb{R}^{3};\mathbb{C}^{4})}\), \({\varepsilon > 0}\), the Sobolev space of order \({3/2+\varepsilon}\) and weight 2. The relation between the time delay operator \({\delta\mathcal{T}\left(f\right)}\) and the Eisenbud–Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented. 相似文献
15.
Via the elementary Darboux transformation (DT) of the modified Kadomtsev--Petviashvili (mKP) equation, a binary Darboux transformation (BDT) of the mKP equation is constructed. 相似文献
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I. Sakalli 《General Relativity and Gravitation》2003,35(8):1321-1335
The Dirac equation is considered in the uniform electromagnetic field space of Bertotti-Robinson with charge coupling. The methods of separation of variables and decoupling are easily achieved. The separated axial equation is reduced to a rare Riccati type of differential equation. The behaviour of potentials, their asymptotic solutions and the conserved currents of the Dirac equation are found. 相似文献
18.
V. S. Kirchanov 《Russian Physics Journal》2014,56(9):1102-1105
19.
With the aid of a gauge transformation, we propose a Darboux transformation for a four-component KdV equation. As an application, we obtain some explicit solutions for the four-component KdV equation. 相似文献
20.
For the KdV equation, the method based upon the Darboux transformation matrix is developed. All the conditions are shown to hold by suitably choosing the constants involved. Exphiit expressions of Darboux matrices are determined in a recursive manner. 相似文献