Quantum Mechanics in Practice: Calculating the Ionization Energy of Helium

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Authors
Walker, Bryan
Issue Date
2020
Type
Presentation
Keywords
Scholarship Sewanee 2020 , Quantum , Hartree , Hartree-Fock , Helium , Hydrogen , Wavefunction , Orbital , Energy
Abstract
Quantum mechanics is a phenomenal tool for modeling the physical world; its predictive power is unparalleled among other quantitative theories in physics. However, the mathematical formalism is a painfully abstract beast that requires considerably more effort than classical theories to extract useful answers in most cases. Here, we will present a method of approximating the quantum-mechanical state of the two nonrelativistic electrons in the ground state of Helium. An exact solution to this motion is unknown because obtaining it involves a PDE over a six-dimensional phase space. However, experience has shown that we can formulate a reasonable guess which converges to a fairly accurate approximation in only a few iterations.
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