Abstract
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.
Highlights
Most physicists are familiar with the Schrödinger equation, which describes the movement of a spin-0 particle with mass (m) moving at speeds much smaller than the speed of light (c) [1] [2] [3] [4] [5]
This equation allows for a quantum description of a constant number of spin-0 particles moving at quasi-relativistic energies
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
Summary
Most physicists are familiar with the Schrödinger equation, which describes the movement of a spin-0 particle with mass (m) moving at speeds much smaller than the speed of light (c) [1] [2] [3] [4] [5]. It should be noted that, if X1 and X2 are two solutions of the time-independent quasi-relativistic wave equation (Equation (20)), respectively corresponding to different kinetic energies K1 and K2, the following wavefunction is a solution of the Klein-Gordon equation:. From this point of view, the time-independent relativistic wave equation should not be considered a fundamental equation, but a useful auxiliar equation for finding solutions of a fundamental Lorentz invariant wave equation satisfying the superposition principle [14]
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