# Topics in Atomic Physics by Burkhardt, Charles E., Leventhal, Jacob J.

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Topics in Atomic Physics

by Burkhardt, Charles E., Leventhal, Jacob J.

2006, XIV, 288 p. 75 illus.

The study of atomic physics propelled us into the quantum age in the early twentieth century and carried us into the twenty-first century with a wealth of new and, in some cases, unexplained phenomena. Topics in Atomic Physics provides a foundation for students to begin research in modern atomic physics. It can also serve as a reference because it contains material that is not easily located in other sources.

A distinguishing feature is the thorough exposition of the quantum mechanical hydrogen atom using both the traditional formulation and an alternative treatment not usually found in textbooks. The alternative treatment exploits the preeminent nature of the pure Coulomb potential and places the Lenz vector operator on an equal footing with other operators corresponding to classically conserved quantities. A number of difficult to find proofs and derivations are included as is development of operator formalism that permits facile solution of the Stark effect in hydrogen.

Discussion of the classical hydrogen atom is also presented. Using the correspondence principle this provides a transition from classical to quantum concepts. It is also adapted to describing certain characteristics of multi-electron atoms.

The book is intended for graduate students who have had introductory quantum mechanics, but undergraduates who have had such a course can also benefit from it. There are more than eighty problems at the ends of chapters with all answers given. A detailed solutions manual, in some cases giving more than one solution, is available to instructors.

Charles E. Burkhardt earned his Ph.D. in experimental atomic physics at Washington University in St. Louis in 1985. He is Professor of Physics at Florissant Valley Community College in St. Louis. Jacob J. Leventhal earned his Ph.D. in experimental atomic physics at the University of Florida in 1965. He is Curators' Professor at the University of Missouri 每 St. Louis. They have collaborated on experimental atomic physics since 1980, publishing numerous papers in research and teaching journals.

Content Level » Graduate

Related subjects » Atomic, Molecular, Optical & Plasma Physics - Quantum Physics

TABLE OF CONTENTS
Background: Introduction.- The Bohr model of the atom.- Numerical values and the fine structure constant.- Atomic dimensions 每 is a reasonable atomic diameter? .- Localizing the electron: Is a point particle reasonable? .- The classical radius of the electron.- Atomic units.- Angular Momentum: Introduction.- Commutators.- Angular momentum raising and lowering operators.- Angular momentum commutation relations with vector operators.- Matrix elements of Vector operators.- Eigenfunctions of orbital angular momentum operators.- Spin.- Angular Momentum - Two Sources: Introduction.- Two sets of quantum numbers - uncoupled and coupled.- Vector model of angular momentum.- Examples of calculation of the Clebsch-Gordan coefficients.- Hyperfine splitting in the hydrogen atom.- The Quantum Mechanical Hydrogen Atom: The radial equation for a central potential.- Solution of the radial equation in spherical coordinates - the energy eigenvalues.- The accidental degeneracy of the hydrogen atom.- Solution of the hydrogen atom radial equation in spherical coordinates - the energy eigenfunctions.- The nature of the spherical eigenfunctions.- Separation of the Schrödinger equation in parabolic coordinates.- Solution of the separated equations in parabolic coordinates - the energy eigenvalues.- Solution of the separated equations in parabolic coordinates - the energy eigenfunctions.- The Classical Hydrogen Atom: Introduction.- The classical degeneracy.- Another constant of the motion - the Lenz vector.- The Lenz Vector and the Accidental Degeneracy: The Lenz vector in quantum mechanics.- Lenz vector ladder operators; conversion of a spherical eigenfunction into another spherical eigenfunction.- Application of the Lenz vector ladder operators to a general spherical eigenfunction.- A new set of angular momentum operators.- Energy eigenvalues.- Relations between the parabolic quantum numbers.- Relationship between the spherical and parabolic eigenfunctions.- Additional symmetry considerations.- Breaking the Accidental Degeneracy: Introduction.- Relativistic correction for the electronic kinetic energy.- Spin-Orbit Correction.- The Darwin Term.- Evaluation of the terms that contribute to the fine-structure of hydrogen.- The total fine structure correction.- The Lamb shift.- Hyperfine structure.- The solution of the Dirac equation.- The Hydrogen Atom in External Fields: Introduction.- The Zeeman effect 每 the hydrogen atom in a constant magnetic field.- Weak electric field - the quantum mechanical Stark effect.- Weak electric field - the classical Stark effect.-The Helium Atom: Indistinguishable particles.- The total energy of the helium atom.- Evaluation of the ground state energy of the helium atom using perturbation theory.- The variational method.- Application of the variational principle to the ground state of helium.- Excited states of helium.- Doubly excited states of helium: autoionization.- Multielectron Atoms: Introduction.- Electron Configuration.- The designation of states - LS coupling.- The designation of states 每 jj coupling.- The Quantum Defect: Introduction.- Evaluation of the quantum defect.- Classical formulation of the quantum defect and the correspondence principle.- The connection between the quantum defect and the radial wave function.- Multielectron Atoms in External Fields: The Stark effect.- The Zeeman effect.- Interaction of Atoms with Radiation: Introduction.- Time dependence of the wave function.- Interaction of an atom with a sinusoidal electromagnetic field.- A two state system 每 the rotating wave approximation.- Stimulated absorption and stimulated emission.- Spontaneous emission.- Angular momentum selection rules.- Selection rules for hydrogen atoms.- Transitions in multi-electron atoms.- Answers to Problems.- Index

Charles E. Burkhardt earned his Ph.D. in experimental atomic physics at Washington University in St. Louis in 1985. He is Professor of Physics at Florissant Valley Community College in St. Louis. Jacob J. Leventhal earned his Ph.D. in experimental atomic physics at the University of Florida in 1965. He is Curators' Professor at the University of Missouri 每 St. Louis. They have collaborated on experimental atomic physics since 1980, publishing numerous papers in research and teaching journals.