Background: Introduction.- The Bohr model of the atom.- Numerical values and the fine structure constant.- Atomic dimensions - 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.- ...
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Background: Introduction.- The Bohr model of the atom.- Numerical values and the fine structure constant.- Atomic dimensions - 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 Schr???dinger 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 quantumnumbers.- 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 - 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 - 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 - 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.-
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