Elementary molecular quantum mechanics. Mathematical methods and applications (Q2849839)

This interesting book is devoted to both the mathematical methods and applications of Quantum Mechanics in Chemistry. The level of the text is such that every student of Physics and Chemistry may understand the main ideas of Quantum Physics. In this book the reader begins with Mathematical Foundations of the Quantum Mechanics. The Hermitian operators and the action of these operators on Hilbert spaces are considered. The basic operators of Quantum Mechanics as angular momentum vector operator, operator of energy (Hamiltonian), operator of Laplace (Laplacian) and so on are introduced along with needed explanations of their properties. The basic ideas of the variational theory as Rayleigh's variational principle, the Ritz method to atomic and molecular systems and a lot of applications are included as well.NEWLINENEWLINEThe perturbation method first introduced by Schrödinger known as the RS perturbation theory is considered with particular explanations. The idea for stationary states up to third order with a short outline of higher orders is discussed. The modification of this theory known as Lennard-Jones-Brillouin-Wigner method is valid also for large perturbations. It is considered the perturbation theory without partitioning of the Hamiltonian known as the symmetry-adapted perturbation theory (SAPT).NEWLINENEWLINEFurthermore, the author considers some basic topics of the differential equations; mainly the Schrödinger equation, its solvability, and its application in the theory of hydrogen atom in electric field. The model of hydrogen molecular ion \(H_2^{+}\) and the Stark effect in atomic hydrogen are discussed as well. Special functions and their applications are considered as well as the Fourier and Laplace transforms applied for solving differential equations. The Padé approximations is also discussed.NEWLINENEWLINEThe eigenvalue problem applied in Hückel's theory of the \(\pi \) electrons of Benzene is shown. The reader may learn further something for the molecular symmetry and applications in the ground state electron configuration of polyatomic molecules.NEWLINENEWLINEThe group theory is given with some applications in Quantum Physics. The theory of many-electron spin, Kotani' synthetic method, and the Löwdin spin projection operators are considered as well.NEWLINENEWLINEHaving in mind all mathematical tools introduced in the first ten chapters, the reader continues with fundamental postulates of Quantum Mechanics, for instance, the correspondence between observables and operators, time evolution of state function, wave-particle dualism and Schrödinger's wave equation. The Born interpretation, measure of observables and orbital model are considered as well.NEWLINENEWLINEThe next Chapter 12 is devoted to atomic orbitals. In Chapter 13 the reader finds some applications of the Variational Calculus for minimizing energy in a quantum system. The next chapters are devoted to the quantum Hamiltonian, many-electron wavefunctions, Hartree-Fock theory for closed shells, valence bond theory and chemical bond, atomic and molecular interactions, and evaluation of molecular integrals.NEWLINENEWLINEChapter 19 is devoted to the relativistic molecular Quantum Mechanics, the Klein-Gordon equation, Dirac's relativistic equation for the electron and theory of spinors. The many-electron atoms and molecules considered as dynamical systems are discussed as well.NEWLINENEWLINEIn the final Chapter 20 one may find the theory of the molecular vibrations, Born-Oppenheimer approximation, Jahn-Teller effect in \(\mathrm{CH}_{4}^{+}\) and conical intersections in polyatomic molecules.NEWLINENEWLINEThe theory to every chapter is illustrated by a set of problems along with their solving that at the same time makes this book very useful not only for students but for scientists and researchers.