Atomic Structure and Quantum Mechanics

  • Fanica Cimpoesu
  • Mihai V. Putz
  • Marilena Ferbinteanu
Chapter

Abstract

Like most books dedicated to structural chemistry, we start with a short recall of the long history leading to current theories of the atomic constitution of matter and the structure of atoms, mentioning Bohr’s crude model and, subsequently, the quantum mechanics frame. A brief introduction to quantum theory, operator and matrix techniques is provided, with annotations explaining the intriguing puzzle of the facts and non-intuitive reasons that contoured this paradigm. The story of Schrödinger’s cat is retold, where the animal is not hurt, replacing the dead or alive states with a sleep versus awake scenario, making the probabilistic paradox quite clear, as a legitimate mixing of wave functions symbolizing the state of the system. The quantum structure of the atom is presented in an original way, i.e. by putting a special emphasis on the effective role in chemistry of Spherical Harmonics functions, grasping the concepts in an intuitive manner, with the help of heuristic symmetry reasons. Taking variable transformations as artifices in the Schrödinger equation of the hydrogen atom, the spectrum of orbital energies unfolds without following through to a complete solution. The chapter offers picturesque descriptions and explanatory artifices which are original, not met in other textbooks. An incursion into the even more mysterious world of relativistic quantum mechanics is made, bringing electron spin into sight, along with related consequences, important for understanding further topics, such as atomic and molecular magnetism. The complexity of the theorization is increased by incorporating the Feynman path integral method, bringing pictures from a territory less often visited by chemists, for the sake of a complete cross-border perspective. Finally, while introducing specific particle and wave representations, as well as their ratio, in quantifying the wave-to-particle quantum information, the basic Heisenberg Uncertainty Relationship (HUR) is recovered for a large range of observable particle-wave Copenhagen duality, although with the dominant wave manifestation, while registering its progressive modification with the factor \(\sqrt {1 - n^{2} }\), in terms of magnitude \(n \in \left[ {0,1} \right]\) of the quantum fluctuation, for the free quantum evolution around the exact wave-particle equivalence.

Keywords

Quantum numbers Quantum operators Schrödinger equation Hamiltonian Matrix method Perturbation theory Atomic shells Spherical harmonics Electronic spin Relativistic quantum chemistry Dirac equation Path integrals Heisenberg uncertainty Wave-particle duality 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Fanica Cimpoesu
    • 1
  • Mihai V. Putz
    • 2
  • Marilena Ferbinteanu
    • 3
  1. 1.Institute of Physical Chemistry “Ilie Murgulescu”BucharestRomania
  2. 2.West University of Timişoara & National Institute of Research and Development for Electrochemistry and Condensed Matter Timişoara (INCEMC)TimişoaraRomania
  3. 3.Department of Inorganic ChemistryUniversity of BucharestBucharestRomania

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