Physics For PHD

Introduction

A PhD in Physics represents the highest level of academic study, focusing on original research and the development of new scientific theories or technologies. Doctoral candidates work on specialized topics such as quantum computing, nuclear physics, astrophysics, or high-energy particle physics. They conduct extensive research, publish scientific papers, and contribute to the global body of physics knowledge. A PhD in Physics prepares individuals for careers in academia, research institutions, and high-tech industries, where they lead innovations and solve some of the most complex scientific challenges.

All Chapters & Topics

1.  Classical mechanics

• 1.1.  Newtonian mechanics
• 1.1.1.  Laws of motion in Newtonian mechanics
• 1.1.2.  Dynamics of particles and systems
• 1.1.3.  Conservation laws
• 1.1.4.  Central force motion
• 1.2.  Lagrangian mechanics
• 1.2.1.  Principle of minimum action
• 1.2.2.  Euler–Lagrange equations
• 1.2.3.  Constraints and normalized coordinates
• 1.2.4.  Noether's theorem
• 1.3.  Hamiltonian mechanics
• 1.3.1.  Hamilton's equations
• 1.3.2.  Canonical conversion
• 1.3.3.  Poisson bracket
• 1.3.4.  Action-angle variable
• 1.4.  Rigid body mobility
• 1.4.1.  Rotation of rigid bodies
• 1.4.2.  Moment of inertia tensor
• 1.4.3.  Euler's equations in rigid body dynamics
• 1.4.4.  Gyroscopic motion
• 1.5.  Chaos and nonlinear dynamics
• 1.5.1.  Stage space and attractive
• 1.5.2.  Bifurcation and chaos theory
• 1.5.3.  Hamiltonian Chaos
• 1.5.4.  Lyapunov exponent

2.  Electrodynamics

• 2.1.  Maxwell's equations
• 2.1.1.  Gauss's law for electricity
• 2.1.2.  Gauss's law for magnetism
• 2.1.3.  Faraday's Law
• 2.1.4.  Ampere's Law
• 2.1.5.  Boundary conditions in Maxwell's equations
• 2.2.  Electromagnetic waves
• 2.2.1.  Wave equation
• 2.2.2.  Polarization
• 2.2.3.  Reflection and Refraction
• 2.2.4.  Waveguides and resonators
• 2.3.  Special relativity
• 2.3.1.  Lorentz transformations
• 2.3.2.  Relativistic energy and momentum
• 2.3.3.  Relativistic electrodynamics
• 2.3.4.  Minkowski spacetime
• 2.4.  Radiation and scattering
• 2.4.1.  Dipole radiation
• 2.4.2.  Multipole expansion
• 2.4.3.  Compton scattering
• 2.4.4.  Thomson and Rayleigh scattering
• 2.5.  Plasma Physics
• 2.5.1.  Debye Screening
• 2.5.2.  Magnetohydrodynamics
• 2.5.3.  Plasma instability
• 2.5.4.  Fusion Plasma

3.  Quantum mechanics

• 3.1.  Foundations of quantum mechanics
• 3.1.1.  Principles of quantum mechanics
• 3.1.2.  Wave function and probability interpretation
• 3.1.3.  Uncertainty principle
• 3.1.4.  Quantum Tunneling
• 3.2.  Schrödinger Equation
• 3.2.1.  Time-dependent Schrödinger equation
• 3.2.2.  Time-independent Schrödinger equation
• 3.2.3.  Eigenvalues and eigenfunctions in the Schrödinger equation
• 3.2.4.  Path integrals in quantum mechanics
• 3.3.  Quantum operators
• 3.3.1.  Commutators and observables
• 3.3.2.  Angular momentum operator
• 3.3.3.  Ladder Operator
• 3.3.4.  Pauli matrices
• 3.4.  Quantum entanglement and measurement
• 3.4.1.  Bell's theorem
• 3.4.2.  Quantum Teleportation
• 3.4.3.  Quantum entanglement and quantum decoherence in measurement
• 3.4.4.  Quantum entanglement and measurement in quantum mechanics
• 3.5.  Relativistic quantum mechanics
• 3.5.1.  Klein–Gordon equation
• 3.5.2.  Dirac equation
• 3.5.3.  Quantum field theory
• 3.5.4.  Feynman path integral

4.  Statistical mechanics and thermodynamics

• 4.1.  Classical thermodynamics
• 4.1.1.  Laws of Thermodynamics
• 4.1.2.  Carnot cycle
• 4.1.3.  Entropy and free energy
• 4.1.4.  Thermodynamic efficiency
• 4.2.  Kinetic theory of gases
• 4.2.1.  Maxwell–Boltzmann distribution
• 4.2.2.  Transport phenomenon
• 4.2.3.  Mean free path
• 4.2.4.  Non-equilibrium systems in the kinetic theory of gases
• 4.3.  Statistical mechanics
• 4.3.1.  Microstates and Macrostates
• 4.3.2.  Partition function
• 4.3.3.  Bose–Einstein and Fermi–Dirac statistics
• 4.3.4.  Fluctuations and correlations
• 4.4.  Phase transition
• 4.4.1.  Important events
• 4.4.2.  Landau theory
• 4.4.3.  Ising model
• 4.4.4.  Renormalization group theory

5.  Quantum field theory

• 5.1.  Second Quantization
• 5.1.1.  Quantum harmonic oscillator in second quantization
• 5.1.2.  Creation and annihilation operators in second quantization
• 5.1.3.  Path Integral in Second Quantization
• 5.1.4.  Fock space
• 5.2.  Quantum Electrodynamics
• 5.2.1.  Feynman diagrams
• 5.2.2.  Renormalization in quantum electrodynamics
• 5.2.3.  Gauge invariance in quantum electrodynamics
• 5.2.4.  Vacuum polarization
• 5.3.  Quantum Chromodynamics
• 5.3.1.  Quarks and gluons
• 5.3.2.  Color range
• 5.3.3.  Lattice QCD
• 5.3.4.  Asymptotic freedom
• 5.4.  Standard model of particle physics
• 5.4.1.  Electroweak theory
• 5.4.2.  Higgs mechanism
• 5.4.4.  Grand Unified Theories

6.  General relativity and gravity

• 6.1.  Einstein's field equations
• 6.1.1.  Ricci tensor and scalar curvature
• 6.1.2.  Schwarzschild solution
• 6.1.3.  Kerr metric
• 6.1.4.  Gravitational waves
• 6.2.  Cosmology
• 6.2.1.  Friedmann equation
• 6.2.2.  Cosmic inflation
• 6.2.3.  Dark matter and dark energy
• 6.2.4.  Large scale structure
• 6.3.  Black holes and wormholes
• 6.3.1.  Event horizon in black holes and wormholes
• 6.3.2.  Hawking radiation
• 6.3.3.  Penrose process
• 6.3.4.  Information paradox in black holes and wormholes

7.  Condensed matter physics

• 7.1.  Crystal structure and lattice
• 7.1.1.  Bravais lattices
• 7.1.2.  Band theory in crystal structure and lattices
• 7.1.3.  Phonons in crystal structure and lattice
• 7.1.4.  Block's theorem
• 7.2.  Superconductivity
• 7.2.1.  BCS principle
• 7.2.2.  Meissner effect
• 7.2.3.  High Temperature Superconductor
• 7.2.4.  Josephson effect