|
Week |
Subject |
Related Preparation |
1) |
The Wentzel – Kramers – Brillouin approximation method. One dimension WKB solutions. Conditions for the validity of the WKB approximation. Turning Point and connection formulas
|
|
2) |
Bound States for Potential wells with No (One, Two) Rigid Walls. Energy levels of a potential well. The "Classical" region. Tunneling through a Potential Barrier.
|
|
3) |
Spin Angular Momentum. Quantum Mechanical Description of the Spin. The Spin Operator, Pauli Matrices, and Spin Angular Momentum Eigenvalues. Quantum Dynamics of a Spin System. Density matrix and Spin Polarization
|
|
4) |
Spin and Rotations. Properties of the Rotation Operator. Representation of the Rotation Operator. Euler Rotations. Spinors
|
|
5) |
The Addition of Angular Momenta. Addition of Two Angular Momenta: General Formalism. Calculation of the Clebsch – Gordan Coefficients. Coupling of Orbital and Spin Angular Momenta.
|
|
6) |
Addition of More than two Angular Momenta. Tensor operators and the Wigner – Eckart Theorem for Spherical Tensor Operators. Reflection Symmetry, Parity, and Time Reversal. Isospin.
Midterm exam I
|
|
7) |
Identical Particles. Many Particle Systems. Symmetrization Postulate. Constructing Symmetric and Antisymmetric Wave Functions.
|
|
8) |
Exchange Degeneracy. Systems of Identical Noninteracting Particles. The Pauli Exclusion Principle. Exclusion Principle and the Periodic Table.
|
|
9) |
Quantum dynamics of Identical Particles. Angular Momentum of System of Identical particles. Angular Momentum and Spin One Half Boson Operators. Helium Atom. Ground State of the helium Atom. First order perturbation theory in many Body Systems. The Hartree – Fock Method
|
|
10) |
The calculus of Variations in Quantum Mechanics. The Rayleigh – Ritz Trial Function. Variation method for Bound States. Variational Form of the eigenvalue problem. Variational calculation of discrete levels. A simple example: The Hydrogen Atom and Harmonic Oscillator. Application to the calculation of excited levels.
|
|
11) |
Spin – orbit forces. LS and jj coupling. The atom in LS coupling. Splitting due to spin – orbital coupling. The normal and anomalous Zeeman Effect. Theory of molecules in adiabatic Approximation. Hydrogen molecule
Midterm exam II
|
|
12) |
Field Quantization. Theory of Radiation. Energy: Momentum and Angular Momentum of the radiation Field. Normal Vibrations. Quantization of the Free Field. Lagrangian of the field. Plane Waves. Photons. Polarization. Emission of a photon by an atom. Dipole emission.
|
|
13) |
Scattering. The Cross Section. The Scattering of a Wave Packet. Scattering Amplitude and Differential Cross Section of Spinless particles. Green’s Functions in Scattering Theory. The Born Approximation. Partial Wave and Phase Shifts. Determination of the Phase Shifts and Scattering Resonances. Phase Shifts and Green’s Functions. Scattering in a Coulomb Field. Partial Wave analysis for Elastic and Inelastic Scattering.
|
|
14) |
Elements of Relativistic Quantum mechanics. The Dirac and Klein – Gordon equations. Dirac theory in the Heisenberg picture. Dirac theory in the Schrödinger Picture and the Nonrelativistic Limit. .Negative Energy solution and positron theory.
|
|