2025
Image Processing: Eigenvalues and Eigenvectors
🧠Objective
This lecture explores the application of eigenvalues and eigenvectors in image processing using Principal Component Analysis (PCA). We will:
Eigenvalues and Eigenvectors of Matrices
Eigenvalues and eigenvectors play a central role in linear algebra, with wide applications in physics, engineering, and data science. They help understand the action of a linear transformation in a given vector space.
Dissertation: N-Interconnected Mass-Spring System
Dissertation-Heat Equation
Simulation of the Heat Equation in a Rectangular Room
Dissertation-Wave Equation
Simulation of the Wave Equation in a Circular Domain Using Python
Classical Mechanics
D’Alembert’s Principle, Lagrange’s Equation and Its Simple Applications
V. Python: Course Contents
🚀 Hands-on Practice: Practice coding by clicking on button below:
IV. Python: Object-Oriented Programming
Object-Oriented Programming (OOP) is a programming style that organizes code into objects, which store data and perform actions. This method makes programs more structured, reusable, and secure. The four main concepts of OOP are:
III. Python: Installation
Python is a high-level, interpreted programming language known for its simplicity and readability. It is widely used in various domains such as web development, data science, artificial intelligence, automation, and more. Python’s syntax is designed to be easy to learn, making it an excellent choice for beginners.
II. Evolution of Programming
“Programming is the art of instructing machines in the language of logic and creativity.”
I. Windows: Basics of Command Prompt
The Command Prompt (cmd.exe) is a command-line interpreter in Windows that allows users to execute commands, run scripts, and perform administrative tasks.
Basic Electronics: Boolean Algebra
Boolean algebra is a mathematical structure used to perform operations on binary variables (0s and 1s). It is fundamental in digital logic design and computer science.
The Concept of Isospin
Isospin is a quantum number that describes the symmetry between particles with similar properties but different electric charges. It was first proposed by Werner Heisenberg in 1932 to explain the near-degeneracy of protons and neutrons. These particles, collectively called nucleons, were found to behave similarly under the strong nuclear force, suggesting an underlying symmetry.
Assignment-I
Instructions:
Explain how complex physical expressions can simplify to exponential decay through Taylor series or other approximations. Provide detailed derivations for the following cases.
Quantum Tunneling
In this article we will study:
Scattering Revisited
In this lecture, we will start by revisiting the basics of quantum scattering, focusing on partial wave analysis and phase shifts. The graph at the top illustrates the Breit-Wigner resonance curve, which we will discuss in detail after exploring resonance scattering and its role in energy-dependent cross-sections.
2024
Nuclear Reactions
Nuclear reactions can occur when a target nucleus $X$ is bombarded by a particle $a$, resulting in a daughter nucleus $Y$ and an outgoing particle $b$:
Basic Electronics: Semiconductors
In 1839, Becquerel discovered that some materials generate an electric current when exposed to light. This is known as the photoelectric effect and is the basis of operations of solar cells. Solar cells are made of semiconductors.
- Note: Semiconductors are materials that act as insulators at low temperatures, but as conductors when energy or heat is available.
Particle Physics: Quarks
Particle Physics: Conservation Laws
The conservation laws of energy, momentum, and charge govern all processes. In particle physics, additional empirical conservation laws are also crucial. They are:
- Conservation of baryon number
- Conservation of lepton number
- Conservation of strangeness
- Conservation of isospin
- Conservation of electric charge
Particle Physics: Particle Classification
Japanese physicist Hideki Yukawa proposed in 1935 that the nuclear force is mediated by a new particle, a meson, whose exchange between nucleons causes the force. He predicted its mass to be about 200 times that of an electron, earning him a Nobel Prize in 1949. Because the new particle would have a mass between that of the electron and that of the proton, it was called a meson (from the Greek meso, “middle”)
Particle Physics Introduction
PG-III Lecture Topics
LASER Rate Equation
Stark Effect in Hydrogen Atom
In the hydrogen atom, the energy levels are determined by the principal quantum number \(n\), and for a given \(n\), the energy is given by:
Approximation Method
Perturbation theory is a powerful tool in quantum mechanics used to study systems where the Hamiltonian can be separated into a known part \(H_0\) and a small perturbation \(H'\). The goal is to find approximate solutions to the Schrödinger equation for the full Hamiltonian \(H = H_0 + H'\) by treating the perturbation as a small correction to the known system.
Scattering
Consider the Hamiltonian $H$ of the system, which is time-independent, given by
Derivations-QM: Current Density Conservation Equation
The Dirac equation for a free particle is given by:
LASER
``` Basic principles and different LASER’s: principles and working of Ruby Laser, He-Ne Laser, Solid state laser, semiconductor laser CO2 LASER and qualitative description of longitudinal and TE- LASER systems, Excimer LASER, Dye LASER, Roman LASER, Plasma recombination LASER.
Tutorial-QM
This tutorial covers Klein-Gordon and Dirac equations in quantum mechanics.
Relativistic Quantum Mechanics
Below is the outline of the lecture on Relativistic Quantum Mechanics, covering the Klein–Gordon equation, Dirac equation, probabilities and current densities, magnetic moment and spin of the electron, and free particle solutions of the Dirac equation.