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The hartree (symbol: E h), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is E h = 4.359 744 722 2060 (48) × 10 −18 J [ 1 ] = 27.211 386 245 981 (30) eV .
In 1959, Shull and Hall [4] advocated atomic units based on Hartree's model but again chose to use as the defining unit. They explicitly named the distance unit a "Bohr radius"; in addition, they wrote the unit of energy as = / and called it a Hartree. These terms came to be used widely in quantum chemistry.
In order to solve the equation of an electron in a spherical potential, Hartree first introduced atomic units to eliminate physical constants. Then he converted the Laplacian from Cartesian to spherical coordinates to show that the solution was a product of a radial function () / and a spherical harmonic with an angular quantum number , namely = (/) (,).
The atomic units were first proposed by Douglas Hartree and are designed to simplify atomic and molecular physics and chemistry, especially the hydrogen atom. [ 18 ] : 349 For example, in atomic units, in the Bohr model of the hydrogen atom an electron in the ground state has orbital radius, orbital velocity and so on with particularly simple ...
Then the square of α is the ratio between the Hartree energy (27.2 eV = twice the Rydberg energy = approximately twice its ionization energy) and the electron rest energy (511 keV). α 2 {\displaystyle \alpha ^{2}} is the ratio of the potential energy of the electron in the first circular orbit of the Bohr model of the atom and the energy m e ...
The ground state energy would then be 8E 1 = −109 eV, where E 1 is the Rydberg constant, and its ground state wavefunction would be the product of two wavefunctions for the ground state of hydrogen-like atoms: [2]: 262 (,) = (+) /. where a 0 is the Bohr radius and Z = 2, helium's nuclear charge.
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In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his numerical skills to Bohr's theory of the atom, for which he obtained his PhD in 1926 – his advisor was Ernest Rutherford. With the publication of Schrödinger's equation in the same year, Hartree was able to apply his knowledge of differential equations and numerical ...