A Notable Quasi-Relativistic Wave Equation and Its Relation to the Schrödinger, Klein-Gordon, and Dirac Equations  

作　　者：Luis Grave de Peralta Hira Farooq Luis Grave de Peralta;Hira Farooq(Department of Physics and Astronomy, Texas Tech University, Lubbock, USA;Nano Tech Center, Texas Tech University, Lubbock, USA)

机构地区：[1]Department of Physics and Astronomy, Texas Tech University, Lubbock, USA [2]Nano Tech Center, Texas Tech University, Lubbock, USA

出　　处：《Journal of Modern Physics》2021年第8期1145-1159,共15页现代物理（英文）

摘　　要：An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schr<span style="white-space:nowrap;">&ouml;</span>dinger and the Klein-Gordon equations, is discussed. This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies. It is shown how to obtain a Pauli-like version of this equation from the Dirac equation. This Pauli-like quasi-relativistic wave equation allows for a quantum description of a constant number of spin-1/2 particles moving at quasi-relativistic energies and interacting with an external electromagnetic field. In addition, it was found an excellent agreement between the energies of the electron in heavy Hydrogen-like atoms obtained using the Dirac equation, and the energies calculated using a perturbation approach based on the quasi-relativistic wave equation. Finally, it is argued that the notable quasi-relativistic wave equation discussed in this work provides interesting pedagogical opportunities for a fresh approach to the introduction to relativistic effects in introductory quantum mechanics courses.An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schr<span style="white-space:nowrap;">&ouml;</span>dinger and the Klein-Gordon equations, is discussed. This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies. It is shown how to obtain a Pauli-like version of this equation from the Dirac equation. This Pauli-like quasi-relativistic wave equation allows for a quantum description of a constant number of spin-1/2 particles moving at quasi-relativistic energies and interacting with an external electromagnetic field. In addition, it was found an excellent agreement between the energies of the electron in heavy Hydrogen-like atoms obtained using the Dirac equation, and the energies calculated using a perturbation approach based on the quasi-relativistic wave equation. Finally, it is argued that the notable quasi-relativistic wave equation discussed in this work provides interesting pedagogical opportunities for a fresh approach to the introduction to relativistic effects in introductory quantum mechanics courses.

关 键 词：Quantum Mechanics Schrödinger Equation Klein-Gordon Equation Dirac Equation Relativistic Quantum Mechanics 

分 类 号：O17[理学—数学]