Four-dimensional atomic structure and law / Kunming Xu.

Format:

Book

Author/Creator:

Xu, Kunming, author.

Series:

Physics Research and Technology Series

Language:

English

Subjects (All):

Atomic structure--Mathematical models.

Atomic structure.

Physical Description:

1 online resource (338 pages)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, Inc., [2023]

Summary:

"A novel spacetime theory is developed to model the atomic structure and the law of electronic motion. Four space dimensions are four geometric elements in a sphere: two periphery points, two semicircular arcs, two hemispherical surfaces, and the inner and outer solid spheres that correspond to the electron octet in a neon shell. The dimension stairs within the atoms are the theoretical basis of electronic orbital quantization in quantum mechanics. The law of nature is dynamic calculus of spherical quantities that defines the motion of an electron from one dimension to another featuring general harmonic oscillation. The fresh mindset will subvert the traditional worldview. Two-dimensional spacetime is described with the instantiation of a helium shell in rigorous mathematics and extended to life phenomena. A husband and a wife are two dimensions of the family; and animals and plants are two kingdoms of the advanced lives. The interplay and transformation between both dimensions are the eternal theme of nature and can be abstracted as a mathematical rope. A DNA molecule, composed of space and time strands, is a stepwise LC oscillatory circuitry or a rope; so is a human lineage with both sexes. Under the four-dimensional space framework, we formulate the wave functions of all electrons within inert atoms. The electronic structure of a chiral carbon conforms to the yin and yang theory and the five element theory in traditional Chinese medicine. It constitutes a physical instance of spherical quantity solutions to three-dimensional Schrödinger's equation. Spherical quantities in dynamic calculus complement physical quantities with linear algebra, comply with the Pythagorean theorem and Maxwell's equations, and characterize the rhythms of entities essentially"-- Provided by publisher.

Contents:

Intro

Contents

Preface

About the Author

Part I. The Atomic Structure

Chapter 1

Spherical Quantities in Two-Dimensional Spacetime

1.1. Introduction

1.2. Euclidean Space and Newtonian Time

1.3. Two-Dimensional Spacetime

1.3.1. General Harmonic Oscillation

1.3.2. Duality in a Helium Shell

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 Definition

1.4.2. Dynamic Calculus Definition

1.4.3. Spacetime Continuity

1.4.4. Properties of Spherical Quantity

1.5. Linear Interpretation of Spherical Quantity

1.5.1. Spherical Quantity as a Rotatory Vector

1.5.2. Dimension Concepts of Space and Time

1.5.3. Spherical Quantities in Euclidean Space

Conclusion

Chapter 2

The Theory of Quaternity

2.1. Introduction to Four Space Dimensions

2.1.1. Four Geometric Elements in a Sphere

2.1.2. Orthogonality and Scalability of Four Space Dimensions

2.2. Quaternity Spacetime

2.2.1. Symmetry and Complementarity of Time and Space

2.2.2. Rotatory Operations in the Quaternity Equation

2.2.3. Electronic Orbitals in a Neon Shell

2.2.4. 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

Chapter 3

Dynamic Calculus in Vector Calculus

3.1. Introduction

3.2. Vector Calculus in One-Dimensional Space

3.3. 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. Orbitals 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. About Quaternity Space

Chapter 4

Quaternity, Relativity, and Quantum Mechanics

4.1. Introduction

4.2. Scope of Views

4.3. Quaternity on EPR Paradox

4.4. Special Relativity in Quaternity

4.5. Quaternity Solutions to Schrödinger's Equations

4.5.1. Duality as a Solution to One-dimensional Schrödinger's Equation

4.5.2. Quaternity as a Solution to Three-dimensional Schrödinger's Equation

Chapter 5

The Structure of Atomic Shells

5.1. Introduction

5.2. Electronic Orbitals in an Argon Shell

5.2.1. Spherical Quantities for 3s3p Electrons

5.2.2. Complementary Orbitals Due to a Clockwise Direction Shift

5.2.3. Dimension Factors as Operators

5.2.4. Electronic Ropes

5.3. Electronic Orbitals in a Krypton Shell

5.3.1. Coordination of Circular Complex Functions

5.3.2. Circular Complex Functions as Exponential Functions

5.3.3. Circular Complex Functions as Radian Angles

5.3.4. Spherical Quantities for 3d Electrons

5.3.5. Complementary Orbitals Due to a Standpoint Shift

5.4. Electronic Orbitals in a Radon Shell and Beyond

5.4.1. Spherical Quantities for 4f Electrons

5.4.2. The Quaternity Periodic Table of Elements

5.4.3. Electronic Interactions and Waves in Atoms

5.4.4. The Atomic Shell Octet

Note from Author

Part II. The Natural Pattern

Chapter 6

Anisotropic 2p Orbitals and a Chiral Carbon

6.1. Introduction to Anisotropic 2p Orbitals

6.1.1. Geometries of 2p Orbitals

6.1.2. Covalent Bonds in Methane, Ethene, and Ethyne.

6.1.3. Nucleophilic Substitutions of Alkyl Halides

6.1.4. Covalent Bonds in Aromatic Rings

6.1.5. Electrophilic Substitutions of Mono-Substituted Benzenes

6.2. Molecular Chirality

6.2.1. The Density Gradient of 2s2p Orbitals

6.2.2. The Origin of Molecular Chirality

6.2.3. The Physical Principle of Optical Rotation

6.2.4. Chiral Disposition Induced by Electrophilic Groups

6.2.5. Selective Electron Transfer through Chiral Centers

Chapter 7

DNA Circuits and Waves

7.1. Introduction

7.2. DNA Electric Conductivity

7.2.1. DNA Electronic Components and Circuitry

7.2.2. Circuit Model Discussion and Prediction

7.3. DNA Wave Functions

7.3.1. Harmonic Oscillation between Base Pairs

7.3.2. Mathematical Formula of DNA

Chapter 8

The Principle of Cells and Life

8.1. Introduction

8.2. The Helium Model for Rope Structure

8.3. The Carbon Model for Gene Expression

8.3.1. DNA Replication (1s to 1s)

8.3.2. DNA Transcription (2s to 2px)

8.3.3. RNA Translation (2px to 2py)

8.3.4. Enzymatic Catalyses (2py to 2pz)

8.3.5. Metabolism and ATP Cycle (2pz to 2s)

8.4. The Zinc Model for Endosymbiotic Organelles

8.5. The DNA Circuitry for the Human Lineage

8.6. Wave Functions as Biological Variables

8.7. The Rotatory Operation for the Mind and Body Relationship

8.8. The Poisson Distribution and Evolution

8.9. The Law of Nature and General Gyroscopes

8.10. At the Dawn of Calculus Biology

Chapter 9

Circular Motion and Central Force

9.1. Introduction

9.2. Kepler's Laws in Atomic Spacetime

9.3. The Energy Density and Coulomb's Law

Chapter 10

The Order of Physical Quantities

10.1. Introduction

10.2. Dimensions of Physical Quantities

10.3. Interpretation of Electromagnetic Quantities.

10.4. The Unification of Physical Quantities

10.5. Dimensions of Thermodynamic Quantities

Chapter 11

The Rational Core of Chinese Medicine

11.1. Introduction to Yin and Yang

11.2. The Common Origin of "Yi Jing" and TCM

11.3. Literal Meanings of Four Spherical Quadrants

11.4. Geometrical Interpretation of Five Elements

11.5. Quaternity Interpretation of Eight Trigrams

Appendix I. Review Questions

Appendix II. Glossary of Key Concepts

Appendix III. The Law of Nature in Mathematics

Appendix IV. Special Meanings of Symbols

References

Index

Blank Page.

Notes:

Description based on print version record.

Includes bibliographical references and index.

Other Format:

Print version: Xu, Kunming Four-Dimensional Atomic Structure and Law

ISBN:

9798891130623