Paper detail

Elimination of angular dependency in quantum three-body problem made easy

This work presents a systematic account of elimination of angular dependency from nonrelativistic Schrödinger equation for a three-body quantum system with arbitrary masses, charges, angular momentum, and parity. The resulting reduced Schrödinger equation (RSE) for the reduced wave components, corresponding to the basis of solid bipolar harmonics, is presented in a compact matrix operator form. The variational form of RSE, providing a practical tool for calculating energy levels and wave functions, is also derived. The resulting angular integrals were derived by expanding bipolar harmonics in a basis of parity-adapted Wigner functions. The theoretical results are numerically validated by computing accurate energy levels for selected states of the helium atom in the explicitly correlated Hylleraas-type basis. The work aims to serve as a self-contained reference for the previously scattered throughout the scientific literature formulation of RSE, offering a convenient foundation for further analytical studies of three-particle quantum systems with arbitrary angular momentum and parity.