Eduardo López, Clara Rojas
We present the study of the one-dimensional Klein-Gordon equation by a smooth barrier. The scattering solutions are given in terms of the Whittaker $M_{κ,μ}(x)$ function. The reflection and transmission coefficients are calculated in terms of the energy, the height and the smoothness of the potential barrier. For any value of the smoothness parameter we observed transmission resonances.
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Recent studies show that deformations in quantum mechanics are inevitable. In this contribution, we consider a relativistic quantum mechanical differential equation in the presence of Dunkl operator-based deformation and we investigate solutions for two important problems in three-dimensional spatial space. To this end, after introducing the Dunkl quantum mechanics, we examine the Dunkl-Klein-Gordon oscillator solutions with the Cartesian and spherical coordinates. In both coordinate systems, we find that the differential equations are separable and their eigenfunctions can be given in terms o…
We solve the Klein-Gordon equation for a step potential with hyperbolic tangent potential. The scattering solutions are derived in terms of hypergeometric functions. The reflection coefficient R and transmission coefficient T are calculated, we observed superradiance and transmission resonances.
We solve the one-dimensional time-independent Klein-Gordon equation in presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker $M_{κ,μ}(x)$ function, and the antiparticle bound state is discussed in terms of potential parameters.
A succinct presentation of the quantized Klein-Gordon field, and a similar quantum presentation of the classical Klein-Gordon random field
量子化克莱因-戈登场的代数结构可以用洛伦兹不变量内积来表示。在非零温度下的经典Klein-Gordon \emph{random}场的表示可以用同样的非对易代数形式给出，允许量子化Klein-Gordon场与经典Klein-Gordon随机场的详细比较。
In this work, we study the generalized Klein-Gordon oscillator with interactions on a curved background within the Kaluza-Klein theory. We solve the generalized Klein-Gordon oscillator in the cosmic string space-time with a linear scalar potential and obtain the energy eigenvalue and corresponding eigenfunction. We show that the energy spectrum depends on the global parameters characterizing the space-time and the confining potential parameter. We also solve the generalized Klein-Gordon oscillator in a magnetic cosmic string background in the Kaluza-Klein theory with a linear scalar potential …
Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field
描述了Klein-Gordon随机场和复Klein-Gordon量子场之间的差异，明确比较了两种理论中测试函数的负频率模式在产生和湮灭算符表述中所起的作用.随机场和复量子场都可以由相同的创造和湮灭算子代数构造，使它们在这个意义上是等价的。
We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.
Further Difficulties with the Klein-Gordon Equation
将Dirac方程与Klein-Gordon方程进行了比较。与Dirac情形不同，本文证明了Klein-Gordon方程在Schroedinger图像的Hamilton算子下存在问题。对Pauli-Weisskopf文章和Feshbach-Villars文章的特别讨论证明，他们关于带电Klein-Gordon粒子的理论缺乏对这个哈密顿量的自洽表达。指出了相关的困难。
(2+3) dimensional geometrical dual of the complex Klein-Gordon equation
本文证明了一个与复Klein-Gordon方程等价的方程可以从（2+3）维Einstein方程耦合到一个守恒的能量动量张量上得到。在一个明确的玩具模型中，我们给出了与复波函数的相位、振幅和质量相对应的匹配条件。
Mechanical interpretation of the Klein-Gordon equation
物理学的基础在微观上可以看作是被直的涡丝从各个方向刺穿的理想流体。被认为是一个孤立的灯丝的小扰动。没有质量的克莱因-戈登方程对应于细丝的弹性拉伸。波函数具有曲线位置矢量的意义。Klein-Gordon方程的质量部分描述了由于弯曲涡丝的流体动力学自感应而导致的螺旋曲线围绕螺旋轴的旋转。
Difficulties with the Klein-Gordon Equation
依赖于变分原理，它被证明是新的矛盾出现从分析的拉格朗日密度的克莱因-戈登场：出现归一化问题和与外部电磁场的相互作用不能发生。相比之下，狄拉克方程没有这些问题。如果把克莱因-戈登场看作经典场，就会产生其他的不一致。
A search on the Klein-Gordon equation
束缚态的s波Klein-Gordon方程被分成两部分，以便在非相对论极限下清楚地看到相对论对解的贡献。并以具体选取的两个算例对模型的可靠性进行了讨论。
On the energy spectrum of the one-dimensional Klein-Gordon Oscillator
在本文中，我们描述了一种方法，引入谐波势的克莱因-戈登方程，导致真正的束缚态。本征函数和本征能量显式计算。
The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the discovery of pions and other subatomic particles. The equation leads to the development of Dirac equation and hence quantum field theory. It shows interesting quantum relativistic phenomena like Klein Paradox and "Zitterbewegung", a rapid vibrating movement of quantum relativistic particles. The simulation of such quantum equations initially motivated Feynman t…
Bound States of the Klein-Gordon Equation for Woods-Saxon Potential With Position Dependent Mass
用Nikiforov-Uvarov方法求解了一维Woods-Saxon势的有效质量Klein-Gordon方程。计算了能量本征值和相应的本征函数。结果也给出了恒定质量的情况下。
Some new solutions to the Klein-Gordon equation in 1-1D space-time in the presence of time dependent potentials
我们在1-1维时空中找到了Klein-Gordon方程在不同含时势下的三个精确解。在两种情况下，我们考虑一个时间依赖的标量势和在一种情况下，时间依赖的电势。
Positive-definite states of a Klein-Gordon type particle
本文提出了Klein-Gordon方程一致概率解释的一种可能途径。假设标量带电粒子的某些态在物理上是不能实现的。其余的量子态被证明具有正定概率分布。
Minimal length of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hyper-geometric functions.
Bound states of the s-wave Klein-Gordon equation with equal scalar and vector Standard Eckart Potential
本文提出了一种求具有相等标量和矢量标准Eckart型势的s波Klein-Gordon方程束缚态解的超对称方法。得到了它的精确解。我们的方法可能的推广概述。
Solutions of the Klein-Gordon equation in an infinite square-well potential with a moving wall
利用双曲空间的变换，我们以一种简单的方法导出了无限方势阱中的Klein-Gordon方程的精确解，该势阱中的边界为常速运动，对于无质量和有质量的情形都是如此.
An Algebraic Method for the Analytical Solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials
通过将波动方程的径向部分简化为二阶微分方程的标准形式，得到了Klein-Gordon方程的解析解。这个标准形式的微分方程是可解的超几何函数，我们给出了一个代数公式的束缚态波函数和能量本征值。这个公式被应用于具有某些双原子势的Klein-Gordon方程的解。
Casimir Effect Associated with Fractional Klein-Gordon Field
本文简要回顾了近年来有关分数克莱因-戈登场的工作，特别是在各种几何形状和边界条件下与分数克莱因-戈登场相关的卡西米尔效应。给出了分数阶Klein-Gordon质量场引起的Casimir活塞的新结果。
Effective-mass Klein-Gordon Equation for non-PT/non-Hermitian Generalized Morse Potential
通过对波函数进行级数展开，求解了实的、非\textrm{PT}对称的、非厄米广义Morse势的一维有效质量Klein-Gordon方程.得到了系统的能量本征值和相应的本征函数。它们也计算了恒定质量的情况下。
We show that the Born's rule is incompatible with Lorentz symmetry of the Square Root Klein-Gordon equation (SRKG equation). It has been demonstrated that the Born rule must be modified in relativistic regime if one wishes to keep the SRKG equation as the correct equation for describing quantum behavior.
Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
在位置相关质量形式下，解析地得到了具有q参数Poschl-Teller势的一维Klein-Gordon方程的能量本征值和相应的本征函数.通过选择质量分布，在计算中使用Nikiforov-Uvarov方法的参数化推广。
The three-dimensional Klein-Gordon oscillator is shown to exhibit an algebraic structure known from supersymmetric quantum mechanics. The supersymmetry is found to be unbroken with a vanishing Witten index, and it is utilized to derive the spectral properties of the Klein-Gordon oscillator, which is closely related to that of the non-relativistic harmonic oscillator in three dimensions. Supersymmetry also enables us to derive a closed-form expression for the energy-dependent Green's function.
In this paper we study the relativistic scalar particle described by the Klein-Gordon interacts with the uniform magnetic field in the context of the Som-Raychaudhuri space-time. Based on the property of the biconfluent Heun function equation, the corresponding Klein-Gordon oscillator and generalized Klein-Gordon oscillator under considering the Coulomb potential are separately investigated, and the analogue of the Aharonov-Bohm effect is analyzed in this scenario. On this basis, we also give the influence of different parameters including the parameter α and oscillator frequency ω, and the po…
We introduce the Dunkl--Klein--Gordon (DKG) equation in 2D by changing the standard partial derivatives by the Dunkl derivatives in the standard Klein--Gordon (KG) equation. We show that the generalization with Dunkl derivative of the $z$-component of the angular momentum is what allows the separation of variables of the DKG equation. Then, we compute the energy spectrum and eigenfunctions of the DKG equations for the 2D Coulomb potential and the Klein--Gordon oscillator analytically and from an ${\rm su}(1,1)$ algebraic point of view. Finally, we show that if the parameters of the Dunkl deriv…
Probability Interpretation for Klein-Gordon Fields and the Hilbert Space Problem in Quantum Cosmology
我们给出了Klein-Gordon场的正定不变内积的一个显式构造，从而解决了Klein-Gordon场的概率解释的老问题，而不必局限于正频率解的子空间.我们的方法有一个更广泛的应用领域，并可用于获得最一般的不变内积的解空间上的一个广泛的类Klein-Gordon型发展方程。我们探讨其后果的解决方案的惠勒-德威特方程与FRW-大质量实标量场模型。
The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
本文证明了球对称引力场的薛定谔-牛顿方程可以从Einstein-Klein-Gordon和Einstein-Dirac系统出发，在1/c的类WKB展开式中导出。
By introducing the scalar potential as modification in the mass term of the Klein-Gordon equation, the influence of a Coulomb-type potential on the Klein-Gordon oscillator is investigated. Relativistic bound states solutions are achieved to both attractive and repulsive Coulomb-type potentials and the arising of a quantum effect characterized by the dependence of angular frequency of the Klein-Gordon oscillator on the quantum numbers of the system is shown.
Exact solution of the Klein Gordon equation in the presence of a minimal length
在存在极小长度的条件下，得到了具有线性向量势和标量势的（1+1）维KleinGordon方程的精确解.本文还研究了该问题的代数方法。
Shape invariance approach to exact solutions of the Klein-Gordon equation
利用形状不变性，我们得到了（1+1）维Klein-Gordon方程在某些类型的标量势和矢量势下的精确解.我们还讨论了在此框架下获得非厄米相互作用实能谱的可能性。
Dynamical symmetries of the Klein-Gordon equation
研究了具有等标量势和矢量势的二维Klein-Gordon方程的动力学对称性。动力学对称性分别考虑在平面和球面上。导出了库仑势对应的SO（3）群和谐振子势对应的SU（2）群的生成元。此外，球体中的生成元构造了希格斯代数。在Casimir算符的帮助下，Klein-Gordon系统的能级被自然地给出.
Exact solutions of Klein Gordon equation for the Makarov potential with the asymptotic iteration method
本文用渐近迭代法导出了Makarov势的Klein-Gordon方程的精确解析解。给出了能量本征值的封闭形式，并利用广义Laguerre多项式和超几何函数得到了相应的归一化本征函数。
This note aims to give prominence to some new results on the absence and localization of eigenvalues for the Dirac and Klein-Gordon operators, starting from known resolvent estimates already established in the literature combined with the renowned Birman-Schwinger principle.
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