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Introduction to Quantum Mechanics

Introduction to Quantum Mechanics. Instructor: Professor Manoj K Harbola, Department of Physics, IIT Kanpur. This is the first course in Quantum Mechanics. The focus of the course is going to be the ideas behind quantum mechanics and its application to simple systems. The course is taught along the lines of development of quantum mechanics so that students get a good feeling about the subject. (from nptel.ac.in)

Introduction


Lecture 01 Black Body Radiation I - Relevant Definitions and Block Body as Cavity
Lecture 02 Black Body Radiation II - Intensity of Radiation in terms of Energy Density
Lecture 03 Black Body Radiation III - Spectral Energy Density and Radiation Pressure inside a Black Body Radiation
Lecture 04 Black Body Radiation IV - Stefan-Boltzmann Law
Lecture 05 Black Body Radiation V - Wien's Displacement Law and Analysis for Spectral Density
Lecture 06 Black Body Radiation VI - Wien's Distribution Law and Rayleigh-Jeans Distribution Law
Lecture 07 Black Body Radiation VII - Quantum Hypothesis and Planck's Distribution Formula
Lecture 08 Radiation as a Collection of Particles called Photons
Lecture 09 Quantum Hypothesis and Specific Heat of Solids
Lecture 10 Bohr's Model of Hydrogen Spectrum
Lecture 11 Wilson Sommerfeld Quantum Condition I - Harmonic Oscillator and Particle in a Box
Lecture 12 Wilson Sommerfeld Quantum Condition II - Particle Moving in a Coulomb Potential in a Plane and Related Quantum Numbers
Lecture 13 Wilson Sommerfeld Quantum Condition III - Particle Moving in a Coulomb Potential in 3D and Related Quantum Numbers
Lecture 14 Quantum Conditions and Atomic Structure, Electron Spin and Pauli's Exclusion Principle
Lecture 15 Interaction of Atoms with Radiation: Einstein's A and B Coefficients
Lecture 16 Stimulated Emission and Amplification of Light in a LASER
Lecture 17 Brief Description of a LASER
Lecture 18 Introduction to the Correspondence Principle
Lecture 19 General Nature of the Correspondence Principle
Lecture 20 Selection Rules (for Transitions) through the Correspondence Principle
Lecture 21 Applications of the Correspondence Principle: Einstein's A Coefficient for the Harmonic Oscillator and the Selection Rules for Atomic Transitions
Lecture 22 Heisenberg's Formulation of Quantum Mechanics: Expressing Kinetic Variables as Matrices
Lecture 23 Heisenberg's Formulation of Quantum Mechanics: The Quantum Condition
Lecture 24 Heisenberg's Formulation of Quantum Mechanics: Application to Harmonic Oscillator
Lecture 25 Brief Introduction to Matrix Mechanics and the Quantum Condition in Matrix Form
Lecture 26 Introduction to Waves and Wave Equation
Lecture 27 Stationary Waves, Eigenvalues and Eigenfunctions
Lecture 28 Matter Waves and Their Experimental Detection
Lecture 29 Representing a Moving Particle by a Wave Packet
Lecture 30 Stationary-state Schrodinger Equation and its Solution for a Particle in a Box
Lecture 31 Solution of Stationary-state Schrodinger Equation for a Simple Harmonic Oscillator
Lecture 32 Equivalence of Heisenberg and the Schrodinger Formulations: Mathematical Preliminaries
Lecture 33 Equivalence of Heisenberg and the Schrodinger Formulations: The x and p Operators and the Quantum Condition
Lecture 34 Born Interpretation of the Wavefunction and Expectation Values of x and p Operators
Lecture 35 Uncertainty Principle and its Simple Applications
Lecture 36 Time Dependent Schrodinger Equation, the Probability Current Density and the Continuity Equation for the Probability Density
Lecture 37 Ehrenfest Theorem for the Expectation Values of x and p Operators
Lecture 38 Solution of Schrodinger Equation for a Particle in One and Two Delta Function Potentials
Lecture 39 Solution of Schrodinger Equation for a Particle in a Finite Well
Lecture 40 Numerical Solution of a One Dimensional Schrodinger Equation for Bound States I
Lecture 41 Numerical Solution of a One Dimensional Schrodinger Equation for Bound States II
Lecture 42 Reflection and Transmission of Particles across a Potential Barrier
Lecture 43 Quantum Tunneling and its Examples
Lecture 44 Solution of the Schrodinger Equation for Free Particles and Periodic Boundary Conditions
Lecture 45 Electrons in a Metal: Density of States and Fermi Energy
Lecture 46 Schrodinger Equation for Particles in Spherically Symmetric Potential, Angular Momentum Operator
Lecture 47 Angular Momentum Operator and its Eigenfunctions
Lecture 48 Equation for Radial Component of the Wavefunction in Spherically Symmetric Potentials and General Properties of its Solution
Lecture 49 Solution for Radial Component of the Wavefunction for the Hydrogen Atom
Lecture 50 Numerical Solution for Radial Component of the Wavefunction for Spherically Symmetric Potentials
Lecture 51 Solution of the Schrodinger Equation for One Dimensional Periodic Potential: Bloch's Theorem
Lecture 52 Kronig-Penney Model and Energy Bands
Lecture 53 Kronig-Penney Model with Periodic Dirac Delta Function and Energy Bands
Lecture 54 Discussion on Bands
Lecture 55 Summary

References
Introduction to Quantum Mechanics
Instructor: Professor Manoj K Harbola, Department of Physics, IIT Kanpur. The focus of the course is going to be the ideas behind quantum mechanics and its application to simple systems.