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1.
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schrödinger-like equation with an effective Rosen–Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation. 相似文献
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Bound states of Klein—Gordon equation for double ring-shaped oscillator scalar and vector potentials 总被引:1,自引:0,他引:1 下载免费PDF全文
In spherical polar coordinates, double ring-shaped oscillator potentials have supersymmetry and shape invariance for θ and r coordinates. Exact bound state solutions of Klein—Gordon equation with equal double ring-shaped oscillator scalar and vector potentials are obtained. The normalized angular wavefunction expressed in terms of Jacobi polynomials and the normalized radial wavefunction expressed in terms of the Laguerre polynomials are presented. Energy spectrum equations are obtained. 相似文献
3.
给出了具有Kratzer型标量势与矢量势的Klein-Gordon方程和Dirac方程的s波束缚态解. 相似文献
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《Physics letters. A》2014,378(32-33):2367-2370
Within the framework of partial-wave method, we study in this Letter the arbitrary l continuum states of the Schrödinger equation with the hyperbolic molecular potential in terms of an improved approximation to the centrifugal term. We present the normalized radial wave functions and obtain analytical formula of phase shifts. In addition, the corresponding bound states are also discussed by studying the analytical properties of the scattering amplitude. We calculate the energy spectra and scattering phase shifts by the improved, previous approximations and the accurate methods, respectively and find that the improved approximation is better than the previous one since the present results are in better agreement with the accurate ones. 相似文献
6.
陈刚 《原子与分子物理学报》2001,18(4):470-472
在标量型和矢量型Morse势相等的条件下,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解.并且在求精确解时,运用一种新的自变量变换方法,使方程求解变得比较简单. 相似文献
7.
Four five‐parametric and five four‐parametric independent confluent Heun potentials for the stationary Klein‐Gordon equation 下载免费PDF全文
We present in total fifteen potentials for which the stationary Klein‐Gordon equation is solvable in terms of the confluent Heun functions. Because of the symmetry of the confluent Heun equation with respect to the transposition of its regular singularities, only nine of the potentials are independent. Four of these independent potentials are five‐parametric. One of them possesses a four‐parametric ordinary hypergeometric sub‐potential, another one possesses a four‐parametric confluent hypergeometric sub‐potential, and one potential possesses four‐parametric sub‐potentials of both hypergeometric types. The fourth five‐parametric potential has a three‐parametric confluent hypergeometric sub‐potential, which is, however, only conditionally integrable. The remaining five independent Heun potentials are four‐parametric and have solutions only in terms of irreducible confluent Heun functions.
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Exact solution of the one-dimensional Klein-Gordon equation with scalar and vector linear potentials in the presence of a minimal length 下载免费PDF全文
Using the momentum space representation, we solve the Klein-Gordon equation in one spatial dimension for the case of mixed scalar and vector linear potentials in the context of deformed quantum mechanics characterized by a finite minimal uncertainty in position. The expressions of bound state energies and the associated wave functions are exactly obtained. 相似文献
10.
在标量势和矢量势相等的条件下,严格求解了在广义非对称Hartmann势场中粒子运动的Klein Gordon方程;并利用束缚态边界条件,获得了束缚态能谱表达式和由超几何函数表示出的波函数. 相似文献
11.
The problem of analytical solutions of the 3-dimensional Dirac equation is usually studied via techniques such as The Nikiforov-Uvarov (NU) method. Here, we see that one of the most attractive potentials can be brought into a well-known form of Schrödinger-like problem possessing known solutions via the methodology of supersymmetry (SUSY). Next, using the idea of shape invariance, we calculate exact solutions of Dirac equation for quadratic scalar and vector potentials in the presence of a tensor potential that depends on the radial component either linearly or inversely. The tensor potential itself, besides its applications, removes degeneracy, too. 相似文献
12.
Within a Pekeris-type approximation to the centrifugal term, we examine the approximately analytical scattering state solutions of the l-wave Schrödinger equation with the modified Rosen-Morse potential. The calculation formula of phase shifts is derived, and the corresponding bound state energy levels are also obtained from the poles of the scattering amplitude. 相似文献
13.
In this paper, using the exponential function transformation approach along with an approximation for the centrifugal potential,
the radial Klein-Gordon equation with the vector and scalar Hulthén potential is transformed to a hypergeometric differential
equation. The approximate analytical solutions of t-waves scattering states are presented. The normalized wave functions expressed in terms of hypergeometric functions of scattering
states on the “k/2π scale” and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solution
is discussed.
相似文献
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The exact solution of the one‐dimensional Klein‐Gordon equation of the ????‐symmetric generalized Woods‐Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s‐states are also investigated for different types of complex generalized Woods‐Saxon potentials. 相似文献
16.
Gao-Feng Wei Xu-Yang Liu Wen-Li Chen 《International Journal of Theoretical Physics》2009,48(6):1649-1658
The approximately analytical scattering state solutions of the l-wave Klein-Gordon equation with the unequal scalar and vector Hulthén potentials are carried out by an improved new approximate
scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Hulthén potentials are presented and the corresponding calculation formula of phase
shifts is derived. It is well shown that the energy levels of the continuum states reduce to those of the bound states at
the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and two
special cases for s-wave (l=0) and for l=0 and equal scalar and vector Hulthén potentials are also studied briefly. 相似文献
17.
We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables. 相似文献
18.
相对论性无自旋粒子在Hartmann势场中运动的精确解 总被引:1,自引:1,他引:0
在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似. 相似文献
19.
Relativistic comparison theorems are established for discrete eigenvalues of Klein-Gordon equation with vector and scalar potentials in d-dimensions. Theorem 1: If V(λ) and S(λ) depend on a parameter λ, ∂S/∂λ?0, S?0, ∂V/∂λ?0, V?0, E>0, then it follows that ∂En/∂λ?0. Theorem 2: If S2?S1?0, 0?V2?V1, E>0, then the corresponding eigenvalues are ordered as En(2)?En(1). Theorem 3: If 0?V2?V1, S2?|S1|, En(1)>0, En(2)>0, then En(2)?En(1). Some illustrative examples are given. 相似文献
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在赝自旋对称性势场中运动的相对论粒子的束缚态 总被引:1,自引:1,他引:0
在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数. 相似文献