Two- and three-body calculations within the dominantly orbital state method

TL;DR

This paper extends the dominantly orbital state method to three-body systems and higher dimensions, providing a semiclassical approach for a broad class of quantum systems with potential applications across various fields.

Contribution

The paper introduces an extension of the dominantly orbital state method to three-body Hamiltonians and higher dimensions, enhancing its applicability and ease of implementation.

Findings

Reliable for large orbital angular momentum and small radial excitations

Can provide spectrum information in specific cases

Applicable to systems with arbitrary kinetic energy and potential

Abstract

The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three identical particles, in $D\ge 2$ dimensions, with arbitrary kinetic energy and potential. This method is very easy to implement and can be used in a large variety of fields. Results are expected to be reliable for large values of the orbital angular momentum and small radial excitations, but information about the whole spectrum can also be obtained in some very specific cases.