Physics of the so q (4) hydrogen atom

Castro, P. G.; Kullock, R.

doi:10.1007/s11232-015-0372-1

Cited by 5 publications

(8 citation statements)

References 27 publications

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“…where in the last equality we used the value of S dS from (31). The result obtained in (32) is consistent [55] with the observed value S gas = (9.5 ± 4.5) × 10 80 .…”

Section: The Hydrogen Gas In De Sitter Spacesupporting

confidence: 84%

“…Given the value α 2 me mp ≃ 2.9 × 10 −8 , it is clear that (37) satisfies the holographic bound (2). As it is shown in [53], the horizon of DeS is a 2-dimensional lattice where the number of cells is equal to the DeS entropy (31). Hence, Eq.…”

Section: The Hydrogen Gas In De Sitter Spacementioning

confidence: 96%

“…This is done (as in the case of a real deformation parameter, q ∈ R, used in Refs. [26,27,28,29,30,31]) by enlarging the corresponding symmetry group, using the Laplace-Runge-Lenz vector, and the separation of so q (4) = su q (2) ⊗ su q (2).…”

Section: Quantum Deformation Of the Hydrogen Atommentioning

confidence: 99%

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On the Hydrogen Atom in the Holographic Universe

Jalalzadeh,

Nejad,

Moniz

2021

Preprint

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We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of the hydrogen atom using the framework of quantum groups. Particularly, the U q (so( 4)) quantum algebra is used to construct a finite-dimensional Hilbert space of the hydrogen atom. As a consequence of the quantum deformation of the hydrogen atom, we demonstrate that the Rydberg constant is dependent on the de Sitter radius, L Λ . This feature is then extended to obtain a finite-dimensional Hilbert space for the full set of all hydrogen atoms in the de Sitter universe. We then show that the dimension of the latter Hilbert space satisfies the holographic bound. We further show that the mass of a hydrogen atom m atom , the total number of hydrogen atoms at the universe, N , and the retrieved dimension of the Hilbert space of neutral hydrogen gas, DimH bulk , are related to the de Sitter entropy, S dS , the Planck mass, m Planck , the electron mass, m e , and the proton mass m p , by m atom ≃ m Planck S − 1 6 dS , N ≃ S 2 3 dS and DimH bulk = 2 me mp α 2 S dS , respectively.

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“…where in the last equality we used the value of S dS from (31). The result obtained in (32) is consistent [55] with the observed value S gas = (9.5 ± 4.5) × 10 80 .…”

Section: The Hydrogen Gas In De Sitter Spacesupporting

confidence: 84%

Section: The Hydrogen Gas In De Sitter Spacementioning

confidence: 96%

See 1 more Smart Citation

On the Hydrogen Atom in the Holographic Universe

Jalalzadeh,

Nejad,

Moniz

2021

Preprint

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“…The hydrogen atom will doubtless continue to be one of testing grounds for fundamental physics. Researchers are exploring the relationship between the hydrogen atom and quantum information [152], the effect of non-commuting canonical variables [x i , x j ] = 0 on energy levels [153][154][155], muonic hydrogen spectra [156], and new physics using Rydberg states [157][158][159][160][161][162]. The ultra high precision of the measurement of the energy levels has led to new understanding of low Z two body systems, including muonium, positronium, and tritium [151].…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

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

Maclay

2020

Symmetry

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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.

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“…Here, we study a q-deformatrion of dynamical symmetry of Hydrogen atom by using the quantum group so 4 q ( ). This is done (as in the case of a real deformation parameter, Î  q , used in [26][27][28][29][30][31]) by enlarging the corresponding symmetry group, using the Laplace-Runge-Lenz vector, and the separation of = Ä so su su 4 2 2 q q q ( ) ( ) ( ). Historically, quantum groups have emerged from studies on quantum integrable models, using quantum inverse scattering methods, which led to deformation of classical matrix groups and their corresponding Lie algebras [32][33][34].…”

mentioning

confidence: 99%

On the hydrogen atom in the holographic universe

Jalalzadeh¹,

Nejad²,

Moniz³

2021

Phys. Scr.

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We investigate the holographic bound utilizing a homogeneous, isotropic, and non-relativistic neutral hydrogen gas present in the de Sitter space. Concretely, we propose to employ de Sitter holography intertwined with quantum deformation of the hydrogen atom using the framework of quantum groups. Particularly, the  q ( so ( 4 ) ) quantum algebra is used to construct a finite-dimensional Hilbert space of the hydrogen atom. As a consequence of the quantum deformation of the hydrogen atom, we demonstrate that the Rydberg constant is dependent on the de Sitter radius, L Λ. This feature is then extended to obtain a finite-dimensional Hilbert space for the full set of all hydrogen atoms in the de Sitter universe. We then show that the dimension of the latter Hilbert space satisfies the holographic bound. We further show that the mass of a hydrogen atom m atom , the total number of hydrogen atoms at the Universe, N, and the retrieved dimension of the Hilbert space of neutral hydrogen gas, Dim  bulk , are related to the de Sitter entropy, S dS , the Planck mass, m Planck , the electron mass, m e , and the proton mass m p , by m atom ≃ m Planck S dS − 1 6 , N ≃ S dS 2 3 and Dim  bulk = 2 m e m p α 2 S dS , respectively.

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Physics of the so q (4) hydrogen atom

Cited by 5 publications

References 27 publications

On the Hydrogen Atom in the Holographic Universe

On the Hydrogen Atom in the Holographic Universe

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

On the hydrogen atom in the holographic universe

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