Special Topics in Atomic Physics
Special Topics in Atomic Physics. Instructor: Prof. P.C. Deshmukh, Department of Physics, IIT Madras. The course will begin with the identification of a complete set of compatible observables for the nonrelativistic Hydrogen atom, identify the complete set of 'good quantum numbers', discuss the associated constants of motion, and associated symmetries. The LaplaceRungeLenz vector and the Fock SO(4) symmetry of the Hydrogen atom will be discussed.
This will be followed by a discussion on coupling of Angular Momenta, ClebschGordan Coefficients, Statement and Proof the WignerEckart Theorem. We shall then discuss the relativistic Hydrogen atom, Dirac equation. FoldyWouthuysen Transformation of Dirac Hamiltonian and Lamb shift. Subsequently, the manyelectron atom will be discussed to acquire an understanding of the HartreeFock SelfConsistent Field Formalism. We shall then examine a Perturbative approach to
relativistic effects; this would provide insight in the relativistic quantum mechanics discussed in an earlier unit based on the Dirac equation.
We shall then proceed to discuss methods to probe the atom. The methods are based on the alternative probes which use quantum collisions of atomic targets with probe particles and probing the atom with an electromagnetic field. We shall discuss the connections of these methods through the timereversal symmetry and obtain the quantum solutions using appropriate boundary conditions. We shall obtain expressions for scattering cross sections, and also for photoionization
crosssection and the angular distribution of the photoelectrons. We shall then examine the quantum mechanics of atoms in external fields and study the Stark effect, and also the family of ZEEMAN effect spectroscopies. A brief introduction to the hyperfine structure and its applications in laser cooling of atoms, BEC, atomic clocks etc. will be pointed out.
(from nptel.ac.in)
Lecture 01  Introduction 
Lecture 02  Quantum Mechanics and Symmetry of the Hydrogen Atom 
Lecture 03  Hydrogen Atom: Rotational and Dynamical Symmetry of the 1/r Potential 
Lecture 04  Hydrogen Atom: Dynamical Symmetry of the 1/r Potential 
Lecture 05  Degeneracy of the Hydrogen Atom: SO(4) 
Lecture 06  Wavefunctions of the Hydrogen Atom 
Lecture 07  Angular Momentum in Quantum Mechanics 
Lecture 08  Angular Momentum in Quantum Mechanics: HalfOddInteger and Integer Quantum Numbers: ................... SU(2) and SO(3) 
Lecture 09  Angular Momentum in Quantum Mechanics: Addition Theorem for Spherical Harmonics, ................... Coupling of Angular Momenta 
Lecture 10  Angular Momentum in Quantum Mechanics: Dimensionality of the DirectProduct (Composite) ................... Vector Space CGC Recursion Relations 
Lecture 11  Angular Momentum in Quantum Mechanics: CGC Matrix, Wigner D Rotation Matrix, ................... Irreducible Tensor Operators 
Lecture 12  Angular Momentum in Quantum Mechanics: More on ITO, and the WignerEckart Theorem 
Lecture 13  Angular Momentum in Quantum Mechanics: WignerEckart Theorem 2 
Lecture 14  Relativistic Quantum Mechanics of the Hydrogen Atom 1 
Lecture 15  Relativistic Quantum Mechanics of the Hydrogen Atom 2 
Lecture 16  Relativistic Quantum Mechanics of the Hydrogen Atom: PAULI Equation, FoldyWouthuysen ................... Transformation 1 
Lecture 17  Relativistic Quantum Mechanics of the Hydrogen Atom: PAULI Equation, FoldyWouthuysen ................... Transformation 2 
Lecture 18  Relativistic Quantum Mechanics of the Hydrogen Atom: FoldyWouthuysen Transformation 3 
Lecture 19  Relativistic Quantum Mechanics of the Hydrogen Atom: Spherical Symmetry of the Coulomb Potential 
Lecture 20  HartreeFock SelfConsistent Field Formalism 1 
Lecture 21  HartreeFock SelfConsistent Field Formalism 2 
Lecture 22  HartreeFock SelfConsistent Field Formalism 3 
Lecture 23  HartreeFock SelfConsistent Field Formalism 4 
Lecture 24  HartreeFock SelfConsistent Field Formalism 5 
Lecture 25  Perturbative Treatment of Relativistic Effects... Schrodinger's and Dirac's QM 
Lecture 26  Perturbative Treatment of Relativistic Effects... Schrodinger's and Dirac's QM 
Lecture 27  Probing the Atom: Collisions and Spectroscopy: Boundary Conditions 1 
Lecture 28  Atomic Probes: Collisions and Spectroscopy: Boundary Conditions 2 
Lecture 29  Atomic Probes: Collisions and Spectroscopy: Scattering Phase Shifts and Boundary Conditions 
Lecture 30  Atomic Probes: Time Reversal Symmetry: Applications in Atomic Collisions and ................... Photoionization Processes 
Lecture 31  Atomic Photoionization cross Sections, Angular Distributions of Photoelectrons 1 
Lecture 32  Atomic Photoionization cross Sections, Angular Distributions of Photoelectrons 2 
Lecture 33  Atomic Photoionization cross Sections, Angular Distributions of Photoelectrons 3 
Lecture 34  Atomic Photoionization cross Sections, Angular Distributions of Photoelectrons 4 
Lecture 35  Atomic Photoionization cross Sections, Angular Distributions of Photoelectrons, ................... CooperZare Formula 
Lecture 36  StarkZeeman Spectroscopy: Stark Effect 
Lecture 37  StarkZeeman Spectroscopy: Stark Effect on n=2 Excited State of the H Atom Zeeman Effect 
Lecture 38  StarkZeeman Spectroscopy: Normal, Anomalous Zeeman Effect; PaschenBack Effect 
Lecture 39  StarkZeeman Spectroscopy: Anomalous Zeeman Effect 
Lecture 40  Zeeman Effect Fine Structure, Hyperfine Structure  Elemental, Rudimentary Introduction to ................... Laser Cooling, BEC, Atomic Clock/ Attosecond Metrology 
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Special Topics in Atomic Physics
Instructor: Prof. P.C. Deshmukh, Department of Physics, IIT Madras. Syllabus. The course will begin with the identification of a complete set of compatible observables for the nonrelativistic Hydrogen atom, ...
