Relativistic Equations

Ajoy Kumar Ghatak, S. Lokanathan

K.H. Tzou

In this paper, as suggested by the classical Hamiltonian equations, a new set of corresponding relativistic equations is set up. Therefrom a relativistic form of Heisenberg's equation is obtained. The relativistic Hamiltonian system of a particle according to the formulation here established has been fully discussed and by following it, however, Dirac's equation appears only naturally as a necessary form of relativistic wave equation for electron in quantum mechanics. The process of taking square root in Dirac's theory is seen to have its classical analogy. Finally, some applications of the relativistic Heisenberg's equation to Dirac's theory have been discussed and it has thereby been pointed out that this equation brings some quantities to being more symmetrical in the relativity sense and also some more general than those the non-relativistic equation can give.

Riccardo D’Auria, Mario Trigiante

Luis Grave de Peralta, Hira Farooq

An intriguing quasi-relativistic wave equation, which is useful between the range of applications of the Schrödinger 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.

Xiang-Yao Wu, Guo, Yiqing, Xin-Guo Yin

In this work, we give the wave equations of relativistic and non-relativistic quantum mechanics which are different from the Schrödinger and Klein-Gordon equation, and we also give the new relativistic wave equation of a charged particle in an electromagnetic field

Egidio Landi Degl’Innocenti