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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 non-relativistic Hydrogen atom, identify the complete set of 'good quantum numbers', discuss the associated constants of motion, and associated symmetries. The Laplace-Runge-Lenz 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, Clebsch-Gordan Coefficients, Statement and Proof the Wigner-Eckart Theorem. We shall then discuss the relativistic Hydrogen atom, Dirac equation. Foldy-Wouthuysen Transformation of Dirac Hamiltonian and Lamb shift. Subsequently, the many-electron atom will be discussed to acquire an understanding of the Hartree-Fock Self-Consistent 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 time-reversal symmetry and obtain the quantum solutions using appropriate boundary conditions. We shall obtain expressions for scattering cross sections, and also for photoionization cross-section 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)

Introduction


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: Half-Odd-Integer 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 Direct-Product (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 Wigner-Eckart Theorem
Lecture 13 - Angular Momentum in Quantum Mechanics: Wigner-Eckart 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, Foldy-Wouthuysen
................... Transformation 1
Lecture 17 - Relativistic Quantum Mechanics of the Hydrogen Atom: PAULI Equation, Foldy-Wouthuysen
................... Transformation 2
Lecture 18 - Relativistic Quantum Mechanics of the Hydrogen Atom: Foldy-Wouthuysen Transformation 3
Lecture 19 - Relativistic Quantum Mechanics of the Hydrogen Atom: Spherical Symmetry of the Coulomb Potential
Lecture 20 - Hartree-Fock Self-Consistent Field Formalism 1
Lecture 21 - Hartree-Fock Self-Consistent Field Formalism 2
Lecture 22 - Hartree-Fock Self-Consistent Field Formalism 3
Lecture 23 - Hartree-Fock Self-Consistent Field Formalism 4
Lecture 24 - Hartree-Fock Self-Consistent 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,
................... Cooper-Zare Formula
Lecture 36 - Stark-Zeeman Spectroscopy: Stark Effect
Lecture 37 - Stark-Zeeman Spectroscopy: Stark Effect on n=2 Excited State of the H Atom Zeeman Effect
Lecture 38 - Stark-Zeeman Spectroscopy: Normal, Anomalous Zeeman Effect; Paschen-Back Effect
Lecture 39 - Stark-Zeeman 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 non-relativistic Hydrogen atom, ...