Overview

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About the course :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.Intended Audience :Physics, Chemistry and Engineering studentsPrerequisites :Basic courses in Calculus, Differential Equations, Mechanics, ElectromagnetismIndustries Support :Content Will be updated soon

Syllabus

Week 1

Black-body radiation and its spectral energy density; black body as a cavity, energy density inside a cavity, radiation pressure
Stefan-Boltzmann law, Wien’s displacement law, Wien’s formula for spectral density
Relation between energy density and average oscillator energy, quantum hypothesis for oscillators and resulting spectral density
More on quantizitaion concept – specific heat of insulators; photoelectric effect
Spectrum of hydrogen atom and Bohr model
Wilson-Sommerfeld quantization condition and application to particle in a box and harmonic oscillator

Week 2

Application of Wilson-Sommerfeld quantization conditions to atoms-I
Application of Wilson-Sommerfeld quantization conditions to atoms-II and quantum numbers
Periodic Table and electron spin
Interaction of light with matter- Einstein’s A and B coefficients
Life-time of an excited-state, LASERS
Towards quantum-mechanics: The correspondence principle

Week 3

The correspondence principle and selection rules
Heisenberg’s formulation of quantum-mechanics I: The variables as matrix elements I
Heisenberg’s formulation of quantum-mechanics II: The quantum condition
Heisenberg’s formulation of quantum-mechanics III: Solution for harmonic oscillator
Matrix mechanics – general discussion
Matrix mechanics – general discussion

Week 4

Introduction to waves and wave equation
Stationary waves and eigenvalues; time-dependence of a general displecement
de Broglie waves and their experimental verification
Representation of a particle as a wavepacket
Time-independent Schrödinger equation; properties of its solutions. Solution for
Solution of Schrodinger equation for particle in a harmonic potential

Week 5

Equivalence of Heisenberg and Schrödinger formulation-I
Equivalence of Heisenberg and Schrödinger formulation-II
Born-interpretation of wavefunction and expectation values
The uncertainty principle and simple applications
Time-depepndent Schrödinger equation and current density
Comparison with Newton’s equations: Ehrenfest’s theorems

Week 6

Examples of solution of one-dimensional Schrödinger equation – Particle in one and two delta function potentials
Solution of one-dimensional Schrödinger equation for particle in a finite well
Numerical solution of one-dimensional Schrödinger equation for bound-states-I
Numerical solution of one-dimensional Schrödinger equation for bound-states-II
Reflection and transmission of particles across a potential barrier
Quantum-tunneling and its examples

Week 7

Solution of Schrödinger equation for free particles and periodic boundary conditions
Electrons in a metal: Density of states, Fermi energy
Schrödinger equation for particles in spherically symmetric potentials, angular momentum operator
Angular momentum operator and its eigenfucntions
Equation for the radial component of wavefunction for spherically symmetric potentials and general properties of its solution
Solution for the radial component of wavefunction for the hydrogen atom

Week 8

Numerical solution for the radial component of wavefunction for spherically symmetric potentials
Solution of Schrodinger equation for one-dimensional periodic potential: Bloch’s theorem
Kroning-Penny model and energy bands
Kroning-Penny model and energy bands
Numerical calculation of bands
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