scholarly journals The energy correction due to a finite size nucleus of the hydrogen atom confined in a penetrable spherical cavity

2018 ◽  
Vol 64 (4) ◽  
pp. 399
Author(s):  
Norberto Aquino ◽  
Alejandro Rojas ◽  
Henry Montgomery Jr.
Keyword(s):  
Hydrogen Atom ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Finite Size ◽  
Point Particle ◽  
Energy Correction ◽  
A Value ◽  
Free Hydrogen ◽  
Uniform Charge Distribution

We computed accurate values for the ground state energy of a hydrogen atom by a finite spherical barrier of height V0 as a function of the confinement radius . We consider the nucleus as a sphere with a uniform charge distribution instead of as a point particle. The contribution to the ground state energy due to the finite nuclear size is computed as a function of the confinement radius,  and the height of the barrier, V0, using time-independent perturbation theory. For an impenetrable cavity with .5 au, we found that this energy correction is fifty times higher than the corresponding value for the free hydrogen atom. For a finite value of V0,we found that the maximum of the energy correction is reached at a value  which very is close to the position at which the electron density is most compact around to the nucleus. This is confirmed though the Shannon entropy in configuration space.

An Interpolating Ansatz for the Ground State of the Spinless Fermion Hamiltonian in D=1 and 2

1997 ◽  
Vol 11 (13) ◽  
pp. 1545-1563
Author(s):  
Miguel A. Martín-Delgado ◽  
Germán Sierra
Keyword(s):  
Critical Point ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Phase Transitions ◽  
Hartree Fock ◽  
Spinless Fermion ◽  
A Value ◽  
Bifurcation Phenomena ◽  
Half Filling

We propose an interpolating ansatz between the strong coupling and weak coupling regimes of a system of spinless interacting fermions in 1D and 2D lattices at half-filling. We address relevant issues such as the existence of Long Range Order, quantum phase transitions and the evaluation of ground state energy. In 1D our method is capable of unveiling the existence of a critical point in the coupling constant at (t/U) c =0.7483 as in fact occurs in the exact solution at a value of 0.5. In our approach this phase transition is described as an example of Bifurcation Phenomena in the variational computation of the ground state energy. In 2D the van Hove singularity plays an essential role in changing the asymptotic behaviour of the system for large values of t/U. In particular, the staggered magnetization for large t/U does not display the Hartree–Fock law [Formula: see text] but instead we find the law [Formula: see text]. Moreover, the system does not exhibit bifurcation phenomena and thus we do not find a critical point separating a CDW state from a fermion "liquid" state.

The Schrödinger–Riccati equation. The ground-state energy of Be I

2002 ◽  
Vol 80 (9) ◽  
pp. 1053-1057 ◽  
Author(s):  
S Fraga ◽  
JM García de la Vega ◽  
E S Fraga
Keyword(s):  
Riccati Equation ◽  
Relative Error ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Maximum Relative Error ◽  
Statistical Calculation ◽  
Absolute Value ◽  
A Value ◽  
Exact Energy

The Schrödinger–Riccati equation has been used for the prediction of the ground-state energy of Be I. A statistical calculation yields a value of –14.670 hartree, with a maximum relative error of 0.02% (in absolute value) with respect to the exact energy of –14.667 36 hartree. PACS Nos.: 31.25Eb, 31.10+z, 02.70-c, 31.15Bs

Atomic ground state energy in multiply connected universes

1980 ◽  
Vol 372 (1749) ◽  
pp. 297-306 ◽  
Keyword(s):  
Hydrogen Atom ◽  
Minkowski Space ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Shift ◽  
Vacuum Fluctuations ◽  
Static Polarizability ◽  
Multiply Connected ◽  
Atomic Ground State

We consider a hydrogen atom interacting with electromagnetic vacuum fluctuations in a variety of multiply connected universes, and calculate, to order e 2 , the shift in energy of its ground state from the value it would take in Minkowski space. The classical dipole self-interaction is also included and, for investigation, we choose universes with underlying manifolds R 1 ⊗ T 3 , R 1 ⊗ B 1 and R 1 ⊗ G 2 upon each of which we impose a flat metric. In all cases, we find the energy shift to be proportional to the atom’s static polarizability.

scholarly journals HOW CAN ONE PROBE PODOLSKY ELECTRODYNAMICS?

2011 ◽  
Vol 26 (21) ◽  
pp. 3641-3651 ◽  
Author(s):  
R. R. CUZINATTO ◽  
C. A. M. DE MELO ◽  
L. G. MEDEIROS ◽  
P. J. POMPEIA
Keyword(s):  
Hydrogen Atom ◽  
Ground State Energy ◽  
Electrostatic Potential ◽  
Ground State ◽  
State Energy ◽  
Inverse Square Law ◽  
Or In Energy ◽  
Set Up

We investigate the possibility of detecting the Podolsky generalized electrodynamics constant a. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis et al. ( Phys. Rev. Lett.99, 200401 (2007)), who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of a. In order to set up bounds for a, we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.

scholarly journals Unparticle contribution to the hydrogen atom ground state energy

2016 ◽  
Vol 759 ◽  
pp. 589-592 ◽  
Author(s):  
Michael F. Wondrak ◽  
Piero Nicolini ◽  
Marcus Bleicher
Keyword(s):  
Hydrogen Atom ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy
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