New exact solution of the one dimensional Dirac Equation for the Woods-Saxon potential within the effective mass case
O. Panella, S. Biondini, A. Arda
备注：
Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures)
We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically.
The quantum engine cycle serves as an analogous representation of classical heat engines for microscopic systems and the quantum regime of thermal devices is composed of a single element. In this work, the Quantum-Mechanical properties of a non-linear quantum oscillator described by the Woods-Saxon [WS] model are examined. The Quantum-Mechanical analogue of the Carnot cycle was constructed using changes in both the width L of the well and the quantum state of the potential well. The efficiency of the quantum engine, consisting of adiabatic and isothermal processes based on the Woods-Saxon [WS]…
Comment on `Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry' [J. Y. Guo and Z-Q. Sheng, Phys. Lett. A 338 (2005) 90]
Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential
Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）；Faculty of Arts and Sciences, Giresun University（吉雷森大学文理学院）；Department of Physics, Karadeniz Technical University（黑海理工大学物理系）
Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator
用具有Uq（3）>SOq（3）对称性的三维q形变谐振子预言的幻数与碱金属原子团簇的实验数据进行了比较（Li，Na，K，Rb，Cs），贵金属（Cu，Ag，Au），二价金属（Zn，Cd）和三价金属（Al，In），以及凝胶模型，Woods-Saxon和酒瓶电势的理论预测，并且涉及使用3 n +1伪量子数的分类方案。在碱金属团簇和贵金属团簇中，三维q变形谐振子正确地预言了实验观测到的所有幻数，直到1500（这是基于电子壳层填充的理论的有效性的预期极限），而另外，它给出了二价金属和三价金属簇的幻数的令人满意的结果，从而表明Uq（3），它是球面（3维各向同性）谐振子的U（3）对称性的非线性扩展，是几个金属团簇系统对称性的良好候选者。与三维q变形谐振子近似产生相同频谱的角动量相关势的泰勒展开式被发现与对称化Woods-Saxon势和酒瓶对称化Woods-Saxon势的泰勒展开式相似，已知它们提供了Ekardt势的成功拟合。
Analytical Solutions of One-Dimensional ($1\mathcal{D}$) Potentials for Spin-0 Particles via the Feshbach-Villars Formalism
Echahid Cheikh Larbi Tebessi University（埃查希德·谢赫·拉比·特贝西大学）；Research Center of Astrophysics and Cosmology, Khazar University（哈萨克斯坦大学天体物理学与宇宙学研究中心）；Departamento de Física, Universidade Federal do Maranhão（马拉尼昂联邦大学物理系）
