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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)

Lecture 39 - Solution of Schrodinger Equation for a Particle in a Finite Well

In this lecture we solve the Schrodinger equation for a particle moving a one-dimensional well of finite height. To facilitate solving the equation, we choose the origin in such a way that the potential is symmetric about it. The non-classical feature of the quantum-mechanical solution is that there is a non-zero probability of finding the particle outside the box. The solution is obtained graphically and it is shown that at least one bound-state always exists in such a potential. The problem is also used to define the strength of the potential. On the basis of this it is shown that quantum-mechanically the strength of the potential depends both on its depth and width. The viewer should try to get the same definition on the basis of uncertainty principle and demanding that the kinetic energy of the particle be such that it is bound.

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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