The hydrogen atom: Quantum mechanics on the quotient of a conformally flat manifold

1980 ◽  
Vol 21 (6) ◽  
pp. 1390-1392 ◽  
Author(s):  
G. A. Ringwood ◽  
J. T. Devreese
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Conformally Flat ◽  
Flat Manifold ◽  
Conformally Flat Manifold

scholarly journals REMARKS ON BIANCHI SUMS AND PONTRJAGIN CLASSES

2014 ◽  
Vol 97 (3) ◽  
pp. 365-382 ◽  
Author(s):  
MOHAMMED LARBI LABBI
Keyword(s):  
Riemannian Curvature ◽  
Conformally Flat ◽  
Flat Manifold ◽  
Equality Case ◽  
Conformally Flat Manifold

AbstractWe use the exterior and composition products of double forms together with the alternating operator to reformulate Pontrjagin classes and all Pontrjagin numbers in terms of the Riemannian curvature. We show that the alternating operator is obtained by a succession of applications of the first Bianchi sum and we prove some useful identities relating the previous four operations on double forms. As an application, we prove that for a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}k$-conformally flat manifold of dimension $n\geq 4k$, the Pontrjagin classes $P_i$ vanish for any $i\geq k$. Finally, we study the equality case in an inequality of Thorpe between the Euler–Poincaré characteristic and the $k{\rm th}$ Pontrjagin number of a $4k$-dimensional Thorpe manifold.

Hypersurfaces in a conformally flat space

2021 ◽  
pp. 2150067
Author(s):  
Sabina Eyasmin
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Shape Operator ◽  
Flat Space ◽  
Conformally Flat ◽  
Flat Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Conformally Flat Manifold ◽  
Proper Generalization

The hypersurface of a space is one of the most important objects in a space. Many authors studied the various geometric aspects of hypersurfaces in a space form. The notion of conformal flatness is one of the most primitive concepts in differential geometry. Again, conformally flat space is a proper generalization of a space form. In this paper, we study the geometry of hypersurfaces in a conformally flat manifold. Then we have investigated some sufficient conditions imposed on the shape operator for which the hypersurface satisfies various pseudosymmetric-type conditions imposed on its conformal curvature tensor.

KOBAYASHI CONFORMAL METRIC ON MANIFOLDS, CHERN-SIMONS AND η-INVARIANTS

1991 ◽  
Vol 02 (04) ◽  
pp. 361-382 ◽  
Author(s):  
BORIS N. APANASOV
Keyword(s):  
Conformal Structure ◽  
Conformally Flat ◽  
Flat Manifold ◽  
Conformal Invariant ◽  
Conformal Class ◽  
Conformal Metric ◽  
Conformally Flat Manifold ◽  
Euclidean Metrics ◽  
Chern Simons

The main aim of this paper is to present a canonical Riemannian smooth metric on a given uniformized conformal manifold (conformally flat manifold) which is compatible with the conformal structure. This metric is related to the Kobayashi construction for complex-analytic manifolds and gives a new conformal invariant. As an application, the paper studies the Chern-Simons functional and the η-invariant associated with the conformal class of conformally-Euclidean metrics on a closed hyperbolic 3-manifold.

Twinkle, Twinkle Little Star

2019 ◽  
pp. 46-53
Author(s):  
Nicholas Mee
Keyword(s):  
Nineteenth Century ◽  
Quantum Mechanics ◽  
Chemical Composition ◽  
Hydrogen Atom ◽  
Periodic Table ◽  
Chemical Properties ◽  
Spectral Lines ◽  
Exclusion Principle ◽  
Middle Years ◽  
Absorption Of Light

The emission and absorption of light by atoms produces discrete sets of spectral lines that were a vital clue to unravelling the structure of atoms and their elucidation was an important step towards the development of quantum mechanics. In the middle years of the nineteenth century Bunsen and Kirchhoff discovered that spectral lines can be used to determine the chemical composition of stars. Following Rutherford’s discovery of the nucleus, Bohr devised a model of the hydrogen atom that explained the spectral lines that it produces. His work was developed further by Pauli, who postulated the exclusion principle in order to explain the structure of other types of atom. This enabled him to explain the layout of the Periodic Table and the chemical properties of the elements.

Quantum Mechanics of the Hydrogen Atom

1987 ◽  
pp. 145-162
Author(s):  
Hermann Haken ◽  
Hans Christoph Wolf
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom

scholarly journals Previously Unknown Physical Formulas which Hold in a Hydrogen Atom and are Derived without Using Quantum Mechanics

2017 ◽  
Vol 9 (4) ◽  
pp. 7
Author(s):  
Koshun Suto
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Hydrogen Atom ◽  
Physical Science ◽  
Classical Quantum ◽  
Physical Quantities

It is thought that quantum mechanics is the physical science describing the behavior of the electron in the micro world, e.g., inside a hydrogen atom. However, the author has previously derived the energy-momentum relationship which holds inside a hydrogen atom. This paper uses that relationship to investigate the relationships between physical quantities which hold in a hydrogen atom. In this paper, formulas are derived which hold in the micro world and make more accurate predictions than the classical quantum theory. This paper concludes that quantum mechanics is not the only theory enabling investigation of the micro world.

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