S. H. Patil, K. T. Tang

Asymptotic Methods in Quantum Mechanics (eBook, PDF)

Application to Atoms, Molecules and Nuclei

• Format: PDF

Produktbeschreibung

Asymptotic Methods in Quantum Mechanics is a detailed discussion of the general properties of the wave functions of many particle systems. Particular emphasis is placed on their asymptotic behaviour, since the outer region of the wave function is most sensitive to external interaction. The analysis of these local properties helps in constructing simple and compact wave functions for complicated systems. It also helps in developing a broad understanding of different aspects of quantum mechanics. As applications, wave functions with correct asymptotic forms are used to systematically generate a large data base for susceptibilities, polarizabilities, interactomic potentials and nuclear densities of many atomic, molecular and nuclear systems.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 174
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642573170
• Artikelnr.: 53393113

Inhaltsangabe

1. Introduction.- 2. General Properties of Wave Functions.- 2.1 Asymptotic Form of Wave Functions.- 2.2 Asymptotic Perturbed Wave Function.- 2.3 Wave Function for rij ? 0.- 2.4 Wave Function for rij and rik ? 0.- 2.5 Local Satisfaction of Schrödinger Equation.- 2.6 Variational Stationary Property.- 2.7 Variational Approach to Perturbations.- 2.8 Generalised Virial Theorem.- 2.9 A Simple Example.- 3. Two- and Three-Electron Atoms and Ions.- 3.1 A Simple Wave Function.- 3.2 Wave Functions Satisfying Cusp, Coalescence and Asymptotic Conditions.- 3.3 Three-Electron Wave Functions.- 4. Polarizabilities and Dispersion Coefficients.- 4.1 Polarizabilities.- 4.2 Dispersion Coefficients.- 4.3 Alkali Isoelectronic Sequences.- 4.4 Asymptotic Polarizabilities and Dispersion Coefficients.- 5. Asymptotically Correct Thomas-Fermi Model Density.- 5.1 Thomas-Fermi Model.- 5.2 Solution for the Thomas-Fermi Density.- 5.3 Asymptotic Density.- 5.4 Modified Density.- 5.5 Applications.- 6. Molecules and Molecular Ions with One and Two Electrons.- 6.1 Wave Functions for One-Electron Molecular Ions.- 6.2 Energies for One-Electron Molecular Ions.- 6.3 Wave Function for H2 and He2++.- 6.4 Results for the Ground State.- 7. Interaction of an Electron with Ions, Atoms, and Molecules.- 7.1 Atomic Rydberg States.- 7.2 Electron-Atom and Electron-Molecule Scattering at High Energies.- 8. Exchange Energy of Diatomic Systems.- 8.1 Exchange Energy of Dimer Ions.- 8.2 Exchange Energy of Diatomic Molecules.- 9. Inter-atomic and Inter-ionic Potentials.- 9.1 Exchange Energy and Exchange Integral in the Heitler-London Theory.- 9.2 Generalized Heitler-London Theory.- 9.3 Inter-atomic and Inter-ionic Potentials.- 10. Proton and Neutron Densities in Nuclei.- 10.1 Semi-phenomenological Density.- 10.2 Determination of the Parameters.- 10.3 Results.- References.

Rezensionen

"This is a monograph ... . It is intended for researchers and graduate students in chemical physics and related areas." (Tuncay Aktosun, zbMATH 0947.81002, 2022)