This chapter begins with a discussion of radiation by a microscopic classical oscillator with radiative damping. It then turns to the Schrödinger equation for the hydrogen atom, and an extended analysis of the solutions to the Schrödinger equation for the hydrogen atom in polar coordinates is then presented. Real orbitals are constructed from linear combinations of the complex Schrödinger equation solutions. The significance of real orbitals for molecular structure and the consequent introduction of rotating and vibrating dipoles are then introduced. A semiclassical model (quantal atom and classical E-M field) for the absorption and emission of radiation is developed and compared to the Einstein A and B coefficients. It is shown how the time-dependence of the radiatively coupled non-stationary states of the hydrogen atom are analogous to the classical harmonic oscillator. The essentials of atomic transitions, as well as molecular rotational, vibrational, and electronic spectroscopy complete the chapter.This chapter begins with a discussion of radiation by a microscopic classical oscillator with radiative damping. It then turns to the Schrödinger equation for the hydrogen atom, and an extended analysis of the solutions to the Schrödinger equation for the hydrogen atom in polar coordinates is then presented. Real orbitals are constructed from linear combinations of the complex Schrödinger equation solutions. The significance of real orbitals for molecular structure and the consequent introduction of rotating and vibrating dipoles are then introduced. A semiclassical model (quantal atom and classical E-M field) for the absorption and emission of radiation is developed and compared to the Einstein A and B coefficients. It is shown how the time-dependence of the radiatively coupled non-stationary states of the hydrogen atom are analogous to the classical harmonic oscillator. The essentials of atomic transitions, as well as molecular rotational, vibrational, and electronic spectroscopy complete the chapter.

Oxford University Press eBooksDec 6, 20120 citations

Notes on quantum mechanics: the Schrodinger Equation

Nielsen, M. P., Laugesen, Jacob, Sanjayan, J. G.

Jan 1, 20010 citations

Introductory Quantum Mechanics II: The Schrödinger Equation

WORLD SCIENTIFIC eBooksJun 1, 20100 citations

Polarization spectroscopy of rubidium atoms: Theory and experiment

Huy Diep, Geol Moon, Heung‐Ryoul Noh

We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the ${D}_{2}$ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.We present a theoretical and experimental study of polarization spectroscopy of rubidium atoms. All of the populations of the magnetic sublevels were calculated from the rate equations and used in the calculation of the polarization spectroscopy spectra. Using this model, we could generate theoretical line shapes of the polarization spectra on the ${D}_{2}$ transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.

Physical Review AMar 27, 200863 citations

Introduction to Quantum Theory and Atomic Structure

P. Anthony Cox

Introduction to Quantum Theory and Atomic Structure envelops the basic concepts needed as background for this topic, and discusses atomic structure but not molecular applications. The first two chapters are concerned with the basic ideas and problems of wave-particle duality, the nature of wavefunction, and its statistical interpretation. Chapter 3 discusses some important applications of Schrödinger's equation to chemically relevant situations. Chapters 4 and 5 deal respectively with the hydrogen atom, and with the structure of many-electron atoms and the periodic table of elements. The emphasis throughout is on the physical concepts and their concrete application.Introduction to Quantum Theory and Atomic Structure envelops the basic concepts needed as background for this topic, and discusses atomic structure but not molecular applications. The first two chapters are concerned with the basic ideas and problems of wave-particle duality, the nature of wavefunction, and its statistical interpretation. Chapter 3 discusses some important applications of Schrödinger's equation to chemically relevant situations. Chapters 4 and 5 deal respectively with the hydrogen atom, and with the structure of many-electron atoms and the periodic table of elements. The emphasis throughout is on the physical concepts and their concrete application.

Oxford University Press eBooksJan 25, 199616 citations

INTRODUCTORY QUANTUM MECHANICS II: THE SCHRÖDINGER EQUATION

WORLD SCIENTIFIC eBooksJan 1, 20100 citations

{D}_{2}

transitions of rubidium atoms. The experimental results demonstrated that our model accurately reproduced spectra for all transitions in hyperfine structures.