Optimización del método de Hartree - Fock para el átomo de helio empleando el método de propagación en espacio de fases de la función de onda electrónica (2024)
The three-body problem has been widely used in physics to describe models consisting of 3 interacting elements, which can be three planets or three particles, such as a nucleus and two electrons. Variational calculation methods show promising results for the helium atom, which possesses these characteristics. However, they use approximations, and new methods are needed to approach the theoretical energy of this atom. We found that with an optimization of the Hartree-Fock method using phase space, better energy was achieved, thanks to the computational efficiency of the Wolfram Mathematica program, thus surpassing the Hartree-Fock limit in fewer iterations. Finally, two models for this atom were studied where, firstly, the angle and distance of the second electron were parameterized. The energy found with this model approached the experimental value with a 0.00447% error. The second model was called particle in a ring, which consists of having the nucleus and the first electron fixed while the second electron orbits around the first electron, where the distance between the electrons (correlation term) is varied, and from this, the wave functions were found for cases where the electron passes near the nucleus to orbiting near the other electron. This allowed us to verify and predict how these particles behave for the helium atom.