Syllabus

Module 1: (7 hours)
Relativity: Galilean relativity and Galilean transformation, Special relativity, Michelson-Morley experiment and postulates of relativity, length contraction and time dilatation, twin paradox, Doppler effect, Lorentz transformation.

Module 2: (5 hours)
Velocity addition, relativistic momentum, mass-energy relation, a brief introduction to general relativity.

Module 3: (6 hours)
Inadequacies in classical physics: Black body radiation, photoelectric effect, X-ray diffraction, Compton Effect, pair production, Davisson-Germer experiment.

Module 4: (7 hours)
Wave-Particle duality: Particle nature of wave, Wave nature of particle, de Broglie waves, group waves, phase velocity & group velocity, uncertainty principle and its application.

Module 5: (12 hours)
Wave functions: probability & wave equation, linearity and superposition of wave functions, expectation values SCHRÖDINGER EQUATION: time-dependent and time-independent SE, eigenvalue & eigenfunctions, boundary conditions on the wave function. Applications of SE: Particle in a box, Finite potential well, tunneling through a barrier, Harmonic oscillator.

The main objective of this course is to show that Newtonian mechanics is an approximation theory, and cannot accurately describe the physical behaviour of our universe. Two regimes where Newtonian mechanics fails to accurately predict the physical outcomes are i) when the bodies are moving near the velocity of light and ii) when the size of the system is relatively small. In this course, we will see that in order to describe these two regimes accurately, we need to understand the ideas of special relativity and quantum mechanics.

To introduce the idea of Einstein's special relativity and to see how special relativity modifies Newtonian mechanics at high velocities.

To introduce various experimental results that lead to the development of quantum mechanics.

To introduce the ideas of wave-particle duality in elementary particles, Uncertainty principles and their applications.

5. To understand Schrödinger’s wave equation, and how to solve them in different physical situations

On completion of the course, the student should have the following learning outcomes
CO1: Newtonian Mechanics is the approximate theory that is valid for small velocity and macroscopic bodies.

CO2: Basics of special relativity and its predictions, such as length contraction, time dilation, mass-energy equivalence, etc.

CO3: The experimental evidences for the inadequacies of classical physics, wave-particle duality, and the idea ofthe uncertainty principle.

CO4: Concept of wave functions and their physical interpretation for matter waves.

CO5: The time-dependent and time-independent Schrödinger equations and their solutions for different potentials.

A. Beiser, A. Beiser, Concept of Modern Physics , Tata-McGraw Hill, 6th edition (2009), Tata Mcgraw Hill.

R. Resnick, Introduction to Special Relativity, Wiley.

R. Resnick and R. Eisberg, Quantum Physics Of Atoms, Molecules, Solids, Nuclei And Particles, 2nd Edition, Wiley.

D. Morin, Special Relativity: For the Enthusiastic Beginner, Createspace Independent Pub.