| Description |
1 online resource |
| Series |
Mathematics research developments |
| Contents |
THE ATOMIC STRUCTURE AND LAW; THE ATOMIC STRUCTURE AND LAW; Library of Congress Cataloging-in-Publication Data; Contents; Preface; Part I. The Atomic Structure; Chapter 1: Spherical Quantities in Two-Dimensional Spacetime; 1.1. Introduction to Spherical Quantity; 1.2. Euclidean Space and Newtonian Time; 1.3. Two-Dimensional Spacetime; 1.3.1. Harmonic Oscillation; 1.3.2. Duality in Helium; 1.3.3. Duality in an LC Circuit; 1.3.4. The Duality Equation vs. Schrödinger's Equation; 1.4. Dynamic Calculus; 1.4.1. Infinitesimal Calculus Review; 1.4.2. Dynamic Calculus; 1.4.3. Spacetime Continuity |
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1.4.4. Properties of Spherical Quantities1.5. Linear Interpretation of Spherical Quantity; 1.5.1. Spherical Quantities by Rotatory Vectors; 1.5.2. Dimension Concepts of Space and Time; 1.5.3. Spherical Quantities in Euclidean Space; 1.6. Introduction to the Spherical View; Chapter 2: The Theory of Quaternity; 2.1. Four Space Dimensions; 2.1.1. Four Geometric Elements in a Sphere; 2.1.2. Orthogonality and Scalability of Four Dimensions; 2.2. Quaternity Spacetime; 2.2.1. Symmetry and Complementarity of Time and Space; 2.2.2. Rotatory Operations and the Quaternity Equation |
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2.2.3. Electronic Orbitals in a Neon Shell2.2.4. Dimension Encapsulation Mechanism; 2.2.5. The Differential Chain Rule; 2.3. Four-Dimensional Harmonic Oscillations; 2.3.1. Harmonic Oscillation in One Dimension; 2.3.2. Harmonic Oscillation in Two Dimensions; 2.3.3. Harmonic Oscillation in Three Dimensions; 2.3.4. Harmonic Oscillation in Four Dimensions; 2.3.5. Four Kinds of Orbital Geometries; 2.4. Compatibility with Classical and Quantum Mechanics; 2.5. Summary; Chapter 3: Dynamic Calculus in Vector Calculus; 3.1. Dynamic Calculus as Vector Calculus Along a Path |
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3.2. Vector Calculus in Two-Dimensional Space3.3. Vector Calculus in Quaternity Space; 3.3.1. The Polor in the First Dimension; 3.3.2. The Metor in the Second Dimension; 3.3.3. The Vitor in the Third Dimension; 3.3.4. The Scalor in the Fourth Dimension; 3.4. Orbital Synchronization; 3.4.1. Green's Theorem; 3.4.2. Stokes' theorem; 3.4.3. Gauss's Theorem; 3.5. Electronic Interaction Through Virtual Photons; 3.6. Summary; Chapter 4: Quaternity, Relativity, and Quantum Mechanics; 4.1. Scope of Views; 4.2. Quaternity on EPR Paradox; 4.3. Special Relativity in Quaternity; 4.4. Summary; References |
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Chapter 5: The Structure of Atomic Shells5.1. Electronic Orbitals in an Argon Shell; 5.1.1. Spherical Quantities for 3s3p Electrons; 5.1.2. Complementary Orbitals due to a Direction Shift; 5.1.3. Dimension Factors as Operators; 5.1.4. Electronic Ropes; 5.2. Electronic Orbitals in a Krypton Shell; 5.2.1. Coordination of Circular Complex Functions; 5.2.2. Circular Complex Functions as Exponential Functions; 5.2.3. Circular Complex Functions as Radian Angles; 5.2.4. Spherical Quantities for 3d Electrons; 5.2.5. Complementary Orbitals Due to a Standpoint Shift; 5.3. Electronic Orbitals in |
| Summary |
This book discovers four-dimensional space within a sphere with the instantiation of the 2s2p electron octet in a neon shell. Four space dimensions correspond to points, lines, planes, and solids geometrically. This book develops the idea of dynamic calculus that is implemented by circular functions instead of infinitesimal limits. As the law of nature, dynamic calculus of spherical quantities describes harmonic oscillations of electrons in atoms by dimension transformation rather than kinematic movement. In particular, electronic orbitals of 1s2s2p within a neon atom are defined in calculus |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Atomic structure -- Mathematical models
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SCIENCE -- Physics -- Quantum Theory.
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Atomic structure -- Mathematical models
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| Form |
Electronic book
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| ISBN |
9781634634670 |
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1634634675 |
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