scholarly journals Bound states of hydrogen atom in a theory with minimal length uncertainty relations

2007 ◽  
Vol 48 (5) ◽  
pp. 053515 ◽  
Author(s):  
J. Slawny
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
Minimal Length ◽  
Uncertainty Relations

scholarly journals 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

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1323 ◽  
Author(s):  
G. Jordan Maclay
Keyword(s):  
Hydrogen Atom ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Bound States ◽  
Integrated Treatment ◽  
Invariance Group ◽  
Elementary Particle Physics ◽  
Background Theory ◽  
Modern Physics ◽  
History Of

Understanding the hydrogen atom has been at the heart of modern physics. Exploring the symmetry of the most fundamental two body system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. In this pedagogic review, we present an integrated treatment of the symmetries of the Schrodinger hydrogen atom, including the classical atom, the SO(4) degeneracy group, the non-invariance group or spectrum generating group SO(4,1), and the expanded group SO(4,2). After giving a 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 discussion of the symmetries, providing explicit expressions for all of the manifestly Hermitian generators in terms of position and momenta operators in a Cartesian space, explaining the action of the generators on the basis states, and giving a unified treatment of the bound and continuum states in terms of eigenfunctions 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 a practical application, the computation of the first order Lamb shift in the hydrogen atom. By using SO(4,2) methods, we are able to obtain a generating function for the radiative shift for all levels. Students, non-experts, and the new generation of scientists may find the clearer, integrated presentation of the symmetries of the hydrogen atom helpful and illuminating. Experts will find new perspectives, even some surprises.

scholarly journals Relationship between the Behavior of Hydrogen and Hydrogen Bubble Nucleation in Vanadium

Materials ◽  
2020 ◽  
Vol 13 (2) ◽  
pp. 322
Author(s):  
Zhengxiong Su ◽  
Sheng Wang ◽  
Chenyang Lu ◽  
Qing Peng
Keyword(s):  
Hydrogen Atom ◽  
First Principles ◽  
Bound States ◽  
Hydrogen Molecule ◽  
Vacancy Cluster ◽  
Bubble Nucleation ◽  
Hydrogen Bubble ◽  
First Principles Calculations ◽  
Hydrogen Atoms ◽  
Macroscopic Deformation

Hydrogen plays a significant role in the microstructure evolution and macroscopic deformation of materials, causing swelling and surface blistering to reduce service life. In the present work, the atomistic mechanisms of hydrogen bubble nucleation in vanadium were studied by first-principles calculations. The interstitial hydrogen atoms cannot form significant bound states with other hydrogen atoms in bulk vanadium, which explains the absence of hydrogen self-clustering from the experiments. To find the possible origin of hydrogen bubble in vanadium, we explored the minimum sizes of a vacancy cluster in vanadium for the formation of hydrogen molecule. We show that a freestanding hydrogen molecule can form and remain relatively stable in the center of a 54-hydrogen atom saturated 27-vacancy cluster.

scholarly journals Hydrogen-atom spectrum under a minimal-length hypothesis

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
Sándor Benczik ◽  
Lay Nam Chang ◽  
Djordje Minic ◽  
Tatsu Takeuchi
Keyword(s):  
Hydrogen Atom ◽  
Minimal Length

scholarly journals Ground state of the hydrogen atom via Dirac equation in a minimal-length scenario

2013 ◽  
Vol 73 (7) ◽  
Author(s):  
T. L. Antonacci Oakes ◽  
R. O. Francisco ◽  
J. C. Fabris ◽  
J. A. Nogueira
Keyword(s):  
Hydrogen Atom ◽  
Dirac Equation ◽  
Ground State ◽  
Minimal Length
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