Quantum Mechanics : Detailed Historical, Mathematical and Computational Approaches book cover
1st Edition

Quantum Mechanics
Detailed Historical, Mathematical and Computational Approaches

ISBN 9780367506339
Published June 16, 2022 by CRC Press
462 Pages 9 Color & 25 B/W Illustrations

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Book Description

Main features:
i) A different approach for teaching Quantum Mechanics encompassing old quantum mechanics, matrix mechanics and wave mechanics in a historical perspective which helps to consolidate most important concepts of Quantum Mechanics;
ii) Original information from the most important papers of Quantum Mechanics;
iii) Derivation of all important equations of Quantum Mechanics, for example, Heisenberg’s uncertainty principle, de Broglie’s wave-particle duality, Schrödinger’s wave equation, etc., showing their interrelations through Dirac’s equations and other applications of matrix and wave mechanics;
iv) Comprehensive mathematical support for the understanding of Quantum Mechanics; derivation of all equations make reading easier;
v) The illustrations of the book cover examples, exercises and do-it-yourself activities;
vi) Fundamentals of Fortran and numerical calculation along with the source codes for numerical solutions of several mathematical and quantum problems. All source codes are in the author’s site: (https://www.fortrancodes.com/);
vii) Chapters devoted to linear algebra and differential equations applied to quantum mechanics and their numerical solutions;
viii) Complete solution for the one-electron and two-electron problems using Schrödinger’s time independent equation along with their source codes.

Table of Contents

Part 1: Computational and Mathematical Support  1. Basics of Fortran  2. Basics of Numerical Calculation and Series  3. Linear Algebra for Quantum Mechanics  4. Differential Equations for Quantum Mechanics  Part 2: Old Quantum Mechanics, Matrix Mechanics and Wave Mechanics  5. Absorption/Emission Spectroscopy and Spectral Lines  6. Black-body Radiation, Einstein and Planck’s Law  7. Bohr, Sommerfeld and Old Quantum Mechanics  8. Heisenberg’s Matrix Quantum Mechanics  9. Wave Packet and de Broglie’s Wave-particle Duality  10. Schrödinger’s Wave Quantum Mechanics  11. Applications of Matrix and Wave Quantum Mechanics  12. Landé, Pauli, Dirac and Spin  13. Boltzmann and Fermi-Dirac Statistics  Part 3: Schrödinger's Solutions to One and Two-electron Problems  14. One-particle Quantum Harmonic Oscillator  15. Particle in a Box  16. Particle in a Circular Motion and Angular Momentum  17. Hydrogen-like Atom and Atomic Orbitals  18. Helium Atom, Variational Method and Perturbation Theory 

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Caio Lima Firme, PhD in Theoretical Chemistry (Doctor of Science) and since 2006 he has been working with Quantum Theory of Atoms in Molecules (QTAIM), Density Functional Theory (DFT), among other methods applied to Organic Chemistry and Inorganic Chemistry. Some equations he developed were the D3BIA aromaticity index, the stability parameters of cyclophanes and the Local Potential Energy Density (LPE) for the analysis of intermolecular interactions and chemical bonds. Some of his important contributions to QTAIM are the linear relation between the delocalization index and formal bond order and the hydrogen-hydrogen bonding applied to alkanes and alkenes. He is Assistant Professor at Federal University of Rio Grande do Norte and had taught Quantum Mechanics and Quantum Chemistry at UFRN. He has one patent and 37 papers so far. Recently, he has written the book Introductory Organic Chemistry and Hydrocarbons: A Physical Chemistry Approach, published by CRC Press/Taylor & Francis Group.