Horchani R, Omugbe E, Njoku I J, Pérez L M, Onate C A, Jahanshir A, Feddi E, Emeje K O, Eyube E S
Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman.
Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria.
Sci Rep. 2024 Nov 19;14(1):28582. doi: 10.1038/s41598-024-80123-9.
The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Rényi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value [Formula: see text] coincides with the 3D [Formula: see text] values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space ([Formula: see text] with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval [Formula: see text] in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions.
在指数型势函数与汤川势函数相互作用下，得到了径向克莱因 - 戈登方程的束缚态解。采用格林 - 奥尔德里奇近似法克服离心势垒，从而得到能量和波函数的解析闭式解。利用傅里叶变换构建了(D)维动量空间波函数。通过两个等价方程推测了位置空间和动量空间的平均值。研究了势参数对期望值和量子信息测量的影响。对于一维情况，结果符合海森堡不确定性原理、费希尔、香农、奥尼塞斯库以及雷尼熵不等式。还验证了其他信息复杂度度量，如香农功率、费希尔 - 香农以及洛佩斯 - 鲁伊斯 - 曼西尼 - 卡尔韦特度量。对于基态，一维动量期望值[公式：见原文]与三维[公式：见原文]值一致，这表明存在简并。由于量子数的维度间简并，一维和三维空间中粒子的总能量可能会出现简并。然而，在当前结果中，一维和三维的简并发生在不同动量区间的固定量子态。因此，在一维中，粒子可以以一定动能穿越整个空间([公式：见原文]，如果它在三维空间中穿越区间[公式：见原文]，其动能必须与之相等。这可能对更高维度的动能简并有影响。
