Ladder Operators for Quantum Systems Confined by Dihedral Angles

TL;DR

This paper constructs ladder operators for quantum systems confined by dihedral angles, enabling the generation of complete eigenfunction bases for harmonic oscillators and hydrogen atoms in various coordinate systems.

Contribution

It introduces new raising and lowering operators for confined quantum systems in multiple coordinate systems, expanding the tools for analyzing such systems.

Findings

Ladder operators for confined harmonic oscillators and hydrogen atoms are explicitly constructed.

Operators enable generation of complete eigenfunction bases in different coordinate systems.

Relationships between eigenfunctions across coordinate systems are established.

Abstract

We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relationships between the eigenfunctions in each pair of coordinates, and with the same eigenenergies are also illustrated.