Abstract
Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms. This includes both, an exact analytical expression for the energies of the bound states, and exact analytical expressions for the wavefunctions, which successfully describe quantum particles with mass and spin-0 up to energies comparable to the energy associated to the mass of the particle. These quasi-relativistic atomic orbitals may be used for improving ab-initio software packages dedicated to numerical simulations in physical-chemistry and atomic and solid-state physics.
Highlights
Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms
Wavefunctions of Hydrogen-like atoms, which are obtained by solving the Schrödinger e quation1–5, are often used in ab-initio quantum mechanics s imulations6–8
This strongly supports the substitution, in abinitio software packages, of the Schrödinger’s radial wavefunctions for the ones which are solutions of Eq [5], when simulations involving the inner electrons of heavy atoms should be conducted. First, it was obtained an exact analytical expression, which allows obtaining the quasi-relativistic energies of the bound states of the electron in Hydrogen-like atoms
Summary
Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms. It is worth restating Eq [25] is an exact result presented here for the first time, while Eq [27] is a well-known approximated r esult. It is worth restating Eq [25] is an exact result presented here for the first time, while Eq [27] is a well-known approximated r esult4,17 This strongly supports the use of the Grave de Peralta equation (this is how the author proposes Eq [5] to be called) for describing quantum particles with mass and spin-0 moving at quasi-relativistic e nergies. The following equation gives the exact energies calculated using the Dirac e quation: En,l,j μc2 1 +
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