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Courses » Introduction to Quantum Mechanics

Introduction to Quantum Mechanics

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 students

Prerequisites

Basic courses in Calculus, Differential Equations, Mechanics, Electromagnetism

Industries that will recognize this course

Content Will be updated soon

ABOUT THE INSTRUCTOR:



Dr. Manoj Kumar Harbola joined the Department in 2000. He obtained his doctoral degree at the City University of New York, USA, working under the supervision of Prof. Viraht Sahni. Subsequently he carried out postdoctoral research at the University of North Carolina, Chapel Hill, USA before joining the Centre for Advanced Technology, Indore as a Scientist.

He is a theoretical physicist, whose chief interest lies in Electronic Structure of Atoms, Molecules and Solids using Density Functional Methods.
Course plan 

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
  • REVIEW
Suggested reading
  • Eisberg and Resnick Quantum Physics
  • Beiser

More details about the course
Course duration : 8 weeks
Start date and end date of course: 20 February 2017-14 April 2017
Date of exam:  23 April, 2017
Time of exam: Shift 1: 9am-12noon; Shift 2: 2pm-5pm
Any one shift can be chosen to write the exam for a course
Final List of exam cities will be available in exam registration form
Registration url - Announcements will be made when the registration form is open for registrations. 
The online registration form has to be filled and the certification exam fee needs to be paid. 
More details will be made available when the exam registration form is published.

CERTIFICATION EXAM:
• The exam is optional for a fee. Exams will be on 23 April 2017.
• Time: Shift 1: 9am-12 noon; Shift 2: 2pm-5pm
• Any one shift can be chosen to write the exam for a course.
• Registration url: Announcements will be made when the registration form is open for registrations.
• The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.

CERTIFICATE:
• Final score will be calculated as : 25% assignment score + 75% final exam score.
• 25% assignment score is calculated as 25% of average of  best 6 out of 8 assignments.
• E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score
  in the final exam with the breakup.It will have the logos of NPTEL and IIT KANPUR. It will be e-verifiable at
nptel.ac.in/noc.