Low-Lying-Spectrum of Hydrogen and Helium Electrons

Hydrogen and helium atom low lying spectrum is obtained and problem of 3 interacting electrons in 1d is addressed numerically.

Low-Lying-Spectrum-Hydrogen-Helium-electrons

MATLAB® Live Script contains numerical solution of basic quantum mechanical problems. Starting with analytically solvable case of hydrogen atom and reproducing numerically low-lying energy spectrum and corresponding wavefunctions, we next study helium atom with two electrons. Even though for helium atom system sizes studied are small (with discrete points in each direction), one can see how explicit numerically exact calculation, without variational approximate methods, suggests shell models to interpret level-structure of many-body problem and leads to parahelium and orthohelium states naturally. The final section is dedicated to constructing many-body wavefucntion obeying Pauli principle for 3 interacting electrons, first with, and then, without decomposing three-body coordinate wavefunctions into the product of single-particle orbitals.

Setup

To Run: Download the Live script and run section by section.

MathWorks Products (https://www.mathworks.com)

Requires MATLAB release R2020a or newer