Physics For Graduate

Introduction

Graduate-level physics involves advanced coursework and research in specialized areas such as condensed matter physics, particle physics, astrophysics, quantum field theory, and advanced electromagnetism. Students engage in independent research, working on theoretical or experimental projects that push the boundaries of scientific knowledge. Computational methods, data analysis, and complex mathematical modeling become essential tools. This phase of study prepares students for careers in academia, industry, and research institutions, where they contribute to cutting-edge discoveries and technological advancements.

All Chapters & Topics

1.  Classical mechanics

• 1.1.  Advanced Kinematics
• 1.1.1.  Generalized coordinate systems
• 1.1.2.  Parametric equations of motion
• 1.1.3.  Non-inertial frames and fictitious forces
• 1.1.4.  Covariant formulation of momentum
• 1.1.5.  Action-angle variable
• 1.2.  Lagrangian and Hamiltonian mechanics
• 1.2.1.  Principle of minimum action
• 1.2.2.  Euler–Lagrange equations
• 1.2.3.  Noether's theorem and conservation laws
• 1.2.4.  Normalized Speed
• 1.2.5.  Canonical conversion
• 1.2.6.  Poisson bracket and Hamilton–Jacobi theory
• 1.2.7.  Hamiltonian chaos and integrability
• 1.3.  Rigid body mobility
• 1.3.1.  Euler's equations of motion
• 1.3.2.  Principal moments of inertia
• 1.3.3.  Gyroscopic motion and precession
• 1.3.4.  Inertia tensor
• 1.3.5.  Stability of rotational speed
• 1.4.  Nonlinear dynamics and chaos
• 1.4.1.  Phase space and stability analysis
• 1.4.2.  Poincaré sections and bifurcation theory
• 1.4.3.  Strange Attractors and Fractals
• 1.4.4.  Lyapunov exponent
• 1.4.5.  KAM theorem and quasi-periodic motion

2.  Electromagnetism

• 2.1.  Advanced Electrodynamics
• 2.1.1.  Green's function and potential theory
• 2.1.2.  Multipole expansion
• 2.1.3.  Image charging method
• 2.1.4.  Boundary conditions and uniqueness theorem
• 2.2.  Electromagnetic wave propagation
• 2.2.1.  Plane waves in dielectrics and conductors
• 2.2.2.  Waveguides and cavity resonators
• 2.2.3.  Radiation pressure and optical tweezers
• 2.2.4.  Polarization and Jones calculus
• 2.3.  Relativistic electrodynamics
• 2.3.1.  Covariant formulation of electrodynamics
• 2.3.2.  Lienard–Wiechert potentials
• 2.3.3.  Synchrotron radiation and bremsstrahlung
• 2.3.4.  Electromagnetic field tensor and Lorentz transformations
• 2.4.  Plasma physics
• 2.4.1.  Magnetohydrodynamics
• 2.4.2.  Debye shielding and plasma oscillations
• 2.4.3.  Alfvén waves and tokamak confinement
• 2.4.4.  Plasma instabilities and turbulence

3.  Statistical mechanics and thermodynamics

• 3.1.  Advanced Thermodynamics
• 3.1.1.  Legendre transforms and thermodynamic potentials
• 3.1.2.  Fluctuation–dissipation theorem
• 3.1.3.  Onsager interpersonal relations
• 3.1.4.  Critical events and phase transitions
• 3.2.  Quantum statistical mechanics
• 3.2.1.  Density Matrix and Ensemble Theory
• 3.2.2.  Bose–Einstein condensates
• 3.2.3.  Quantum phase transition
• 3.2.4.  Fermi–Dirac and Bose–Einstein statistics
• 3.2.5.  Partition functions and grand canonical ensembles

4.  Quantum mechanics

• 4.1.  Advanced wave mechanics
• 4.1.1.  WKB approximation
• 4.1.2.  Path integral formulation
• 4.1.3.  Quantum harmonic oscillator and coherent states
• 4.2.  Angular momentum and spin
• 4.2.1.  Spherical Harmonics
• 4.2.2.  Clebsch–Gordan coefficient
• 4.2.3.  Wigner–Eckart theorem
• 4.2.4.  Spin–orbit coupling
• 4.3.  Quantum scattering theory
• 4.3.1.  Born approximation
• 4.3.2.  Partial wave analysis
• 4.3.3.  Optical theorem
• 4.3.4.  S-matrix theory
• 4.4.  Quantum field theory
• 4.4.1.  Second Quantization
• 4.4.2.  Feynman diagrams and propagators
• 4.4.3.  Renormalization theory
• 4.4.4.  Gauge theory and Yang–Mills fields
• 4.4.5.  Spontaneous symmetry breaking and the Higgs mechanism

5.  General relativity and cosmology

• 5.1.  Tensor calculus and differential geometry
• 5.1.1.  Einstein field equations
• 5.1.2.  Schwarzschild and Kerr metrics
• 5.1.3.  Geodesics and Christoffel symbols
• 5.2.  Cosmology and the Universe
• 5.2.1.  The FLRW metric and cosmic inflation
• 5.2.2.  Dark energy and structure formation
• 5.2.3.  Cosmic microwave background radiation

6.  Condensed matter physics

• 6.1.  Band structure and transport theory
• 6.1.1.  Block theorem and the Kronig–Penney model
• 6.1.2.  Fermi surface topology
• 6.1.3.  Quantum Hall Effect
• 6.2.  Superconductivity
• 6.2.1.  BCS theory and Cooper pairs
• 6.2.2.  Meissner effect and flux quantization
• 6.2.3.  The Josephson Effect and SQUIDs
• 6.3.  Topological phases of matter
• 6.3.1.  Topological Insulators
• 6.3.2.  Majorana fermions in topological phases of matter

7.  Nuclear and Particle Physics

• 7.1.  Quantum Chromodynamics (QCD)
• 7.1.1.  Quark–gluon plasma
• 7.1.2.  Asymptotic freedom
• 7.1.3.  Confinement and hadronization
• 7.2.  Beyond the Standard Model
• 7.2.1.  Grand Unified Theories
• 7.2.2.  Supersymmetry and extra dimensions
• 7.2.3.  Neutrino oscillations