English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Understanding the hydrogen atom has been at the heart of modern physics.Exploring the symmetry of the most fundamental two body system has led toadvances in atomic physics, quantum mechanics, quantum electrodynamics, andelementary particle physics. In this pedagogic review we present an integratedtreatment of the symmetries of the Schrodinger hydrogen atom, including theclassical atom, the SO(4) degeneracy group, the non-invariance group orspectrum generating group SO(4,1) and the expanded group SO(4,2). After givinga brief history of these discoveries, most of which took place from 1935-1975,we focus on the physics of the hydrogen atom, providing a background discussionof the symmetries, providing explicit expressions for all the manifestlyHermitian generators in terms of position and momenta operators in a Cartesianspace, explaining the action of the generators on the basis states, and givinga unified treatment of the bound and continuum states in terms ofeigenfunctions that have the same quantum numbers as the ordinary bound states.We present some new results from SO(4,2) group theory that are useful in apractical application, the computation of the first order Lamb shift in thehydrogen atom. By using SO(4,2) methods, we are able to obtain a generatingfunction for the radiative shift for all levels. Students, non-experts and thenew generation of scientists may find the clearer, integrated presentation ofthe symmetries of the hydrogen atom helpful and illuminating. Experts will findnew perspectives, even some surprises.

Dynamical Symmetries of the H Atom, One of the Most Important Tools Of  Modern Physics: SO(4) to SO(4,2), Background, Theory, and Use in Calculating  Radiative Shifts