Abstract
Using a novel wave equation, which is Galileo invariant but can give precise results up to energies as high as mc2, exact quasi-relativistic quantum mechanical solutions are found for the Hydrogen atom. It is shown that the exact solutions of the Grave de Peralta equation include the relativistic correction to the non-relativistic kinetic energies calculated using the Schrödinger equation.
Highlights
Quantum mechanics triumphed when physicists learned to describe the quantum states of the electrons in the atoms by solving the Schrödinger equation [1] [2] [3] [4] [5]
The Schrödinger equation is not Lorentz invariant but Galilean invariant [6] [7]; a relativistic quantum mechanics cannot be based on the Schrödinger equation
It has been shown how to solve the Grave de Peralta equation for a charged quantum particle with mass and spin-0, which is moving in a Coulomb potential or contained in a spherical infinite well
Summary
Quantum mechanics triumphed when physicists learned to describe the quantum states of the electrons in the atoms by solving the Schrödinger equation [1] [2] [3] [4] [5]. Wave mechanics triumphed when Schrödinger, using his equation, was able to reproduce the results previously obtained by Bohr for the energies of the bound states of the electron in the Hydrogen atom. This was possible because the electron in the Hydrogen atom moves at non-relativistic energies [1] [2] [3] [4] [5]. The use of the Grave de Peralta equation is explored [7] [11], which is a quasi-relativistic wave equation, for describing the bounded states of an electron in a Hydrogen-like atom with atomic number Z. The conclusions of this work are given in the last section
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