Mathematical analysis of a Bohr atom model

Chen, Goong; Ding, Zegang; Hsu, Sze-Bi; Kim, Moochan; Zhou, Jianxin

doi:10.1063/1.2168396

Cited by 10 publications

(7 citation statements)

References 13 publications

(14 reference statements)

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“…These calculations involve a simple minded minimization of classical functionals of the type considered by Bohr in 1913. Mathematical justification of such a procedure was found by Chen et al [13] The accuracy of results obtained with help of such classical calculations (employing however the B-S quantization rule !) compares well with incomparably more elaborate traditional quantum mechanical calculations.…”

Section: -Body Problem and The He Atom (Modern Perspective)mentioning

confidence: 99%

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Quantum Signatures of Solar System Dynamics

Kholodenko

2007

Preprint

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Let ω(i) be period of rotation of the i-th planet around the Sun (or ω j (i) be period of rotation of j-th satellite around the i-th planet). From empirical observations it is known that within margins of experimental errors i n i ω(i) = 0 (or j n j ω j (i) = 0) for some integers n i (or n j ), different for different satellite systems. These conditions, known as resonance conditions, make uses of theories such as KAM difficult to implement. The resonances in Solar System are similar to those encountered in old quantum mechanics where applications of methods of celestial mechanics to atomic and molecular physics were highly successful. With such a successes, the birth of new quantum mechanics is difficult to understand. In short, the rationale for its birth lies in simplicity with which the same type of calculations can be done using methods of quantum mechanics capable of taking care of resonances. The solution of quantization puzzle was found by Heisenberg. In this paper new uses of Heisenberg's ideas are found. When superimposed with the equivalence principle of general relativity, they lead to quantum mechanical treatment of observed resonances in the Solar System. To test correctness of theoretical predictions the number of allowed stable orbits for planets and for equatorial stable orbits of satellites of heavy planets is calculated resulting in good agreement with observational data. In addition, the paper briefly discusses quantum mechanical nature of rings of heavy planets and potential usefulness of the obtained results for cosmology. Key wordsHeisenberg honeycombs • Quantum and celestial mechanics • Group theory • Exactly solvable classical and quantum dynamical problems • Equivalence principle • Cosmological constant •(anti) de Sitter spaces

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Section: -Body Problem and The He Atom (Modern Perspective)mentioning

confidence: 99%

“…It follows that each permutation is a constant of motion. This happens even if the Hamiltonian is not constant 13 ." At this point it is important to recall the famous theorem by Caley [37] which states that "every finite group is isomorphic to some permutation group".…”

Section: General Commentsmentioning

confidence: 99%

Quantum Signatures of Solar System Dynamics

Kholodenko

2007

Preprint

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“…In the Bohr's theory, the circular orbital length is equal to a integer times the wavelength of the electron, so we have, 2πr = n × h/mv. In several phenomena, the Bohr's model provides good accuracy [4,5,6]. But this model could not explain about the spin of the electron and the two-electron atoms such as the helium exactly.…”

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confidence: 99%

Calculation of Helium Ground State Energy by Bohr's Theory-Based Methods

Tsubono

2009

Preprint

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Bohr's model agreed with the hydrogen spectrum results, but did not agree with the spectrum of Helium. Here we show that Bohr's model-based methods can calculate the experimental value (-79.005 eV) of Helium ground state energy correctly. we suppose the orbital planes of the two electrons are perpendicular to each other. By a computational method, we calculate the Coulomb force among the particles, and the number of de Broglie's waves contained in the short segment at short time intervals. Our results demonstrate that two electrons of Helium are actually moving around, not as electron clouds.

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“…To put issues in perspective, Bohr's semiclassical theory of electronic structure may be applied to molecules and is known to deliver more accurate results than comes from many modern sophisticated DFT approaches. [308][309][310][311][312] The advantage of Bohr's approach is that it includes electron correlation simply and easily. Indeed, we have shown that a range of basic chemical phenomena like the nature of the valence states of transition-metal compounds, f-block chemistry, the basic description of NMR spectroscopy, relativistic effects in chemistry, etc., can be simply described at this level, providing an easy way to explain chemistry to freshman students.…”

Section: Strong But Highly Distributed Electron Correlation: the Van mentioning

confidence: 99%

Putting David Craig’s Legacy to Work in Nanotechnology and Biotechnology

Reimers¹

2016

Aust. J. Chem.

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left us with a lasting legacy concerning basic understanding of chemical spectroscopy and bonding. This is expressed in terms of some of the recent achievements of my own research career, with a focus on integration of Craig's theories with those of Noel Hush to solve fundamental problems in photosynthesis, molecular electronics (particularly in regard to the molecules synthesized by Maxwell Crossley), and self-assembled monolayer structure and function. Reviewed in particular is the relation of Craig's legacy to: the 50-year struggle to assign the visible absorption spectrum of arguably the world's most significant chromophore, chlorophyll; general theories for chemical bonding and structure extending Hush's adiabatic theory of electron-transfer processes; inelastic electron-tunnelling spectroscopy (IETS); chemical quantum entanglement and the Penrose-Hameroff model for quantum consciousness; synthetic design strategies for NMR quantum computing; Gibbs free-energy measurements and calculations for formation and polymorphism of organic self-assembled monolayers on graphite surfaces from organic solution; and understanding the basic chemical processes involved in the formation of gold surfaces and nanoparticles protected by sulfur-bound ligands, ligands whose form is that of Au 0 -thiyl rather than its commonly believed Au I -thiolate tautomer.

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Mathematical analysis of a Bohr atom model

Cited by 10 publications

References 13 publications

Quantum Signatures of Solar System Dynamics

Quantum Signatures of Solar System Dynamics

Calculation of Helium Ground State Energy by Bohr's Theory-Based Methods

Putting David Craig’s Legacy to Work in Nanotechnology and Biotechnology

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