course outline

Assignment 4_2: Course outline of the subject

B.Sc. (H)

1.     Course Name: Introduction to Quantum mechanics

Theory: 60 hours

Credit: 75 marks

2.     Pre-requisites: Before study this course student should know basic concepts of classical mechanics

3.     Instructors detail: Name: xyz

Contact : 974893xxxx

4.     Course Objective

Ø  The objective of this course is to teach the physical and mathematical foundations necessary for learning various topics in quantum mechanics which are crucial for understanding atoms, molecules or subatomic particles. After developing the basic foundation on physical and mathematical concepts, more advanced concepts in quantum physics and their applications to subatomic particles are discussed. 

5.     Course Learning Outcomes  

After getting exposure to this course, the following topics would be learnt:

Ø  Main aspects of the inadequacies of classical mechanics as well as understanding of the historical development of quantum mechanics.

Ø  Formulation of Schrodinger equation and the idea of probability interpretation associated with wave-functions.

Ø  Methods to solve time-dependent and time-independent Schrodinger equation.

Ø  Quantum mechanics of simple harmonic oscillator.

Ø  Non-relativistic hydrogen atom: spectrum and eigenfunctions

Ø  Application to atomic systems

6.     Distribution of syllabus

Unit 1

Wave-particle duality of particle and wave: Planck’s quantum, Planck’s constant and light as a collection of photons; Blackbody Radiation: Quantum theory of Light; Photo-electric effect and Compton scattering. De Broglie wavelength and matter waves; Davisson-Germer experiment. Wave description of particles by wave packets. Group and Phase velocities and relation between them. Double-slit experiment with electrons. Probability. Wave amplitude and wave functions.

(11 Lectures)

Unit 2

Heisenberg Uncertainty theory: gamma ray microscope thought experiment; Wave-particle duality leading to Heisenberg uncertainty principle; Uncertainty relations involving canonical pair of variables: Derivation from Wave Packets; Impossibility of a particle following a trajectory; Estimating minimum energy of a confined particle using uncertainty principle; Energy-time uncertainty principle: origin of natural width of emission lines as well as estimation of the mass of the virtual particle that mediates a force from the observed range of the force

(8 Lectures)

Unit 3

Schrodinger wave equations: Two-slit interference experiment with photons, atoms and particles; linear superposition principle as a consequence; Schrodinger equation for non-relativistic particles; Momentum and Energy operators; stationary states; physical interpretation of a wave function, probabilities and normalization; Probability and probability current densities in one dimension.

(10 Lectures)

Unit 4

Application of time independent Schrodinger wave equation: One dimensional infinitely rigid box: energy eigenvalues, eigenfunctions and their normalization; Quantum dot as an example; Quantum mechanical scattering and tunneling in one dimension: across a step potential & across a rectangular potential barrier. one- dimensional problem-square well potential; Quantum mechanics of simple harmonic oscillator: energy levels and energy eigenfunctions using Frobenius method; Hermite polynomials; ground state, zero point energy & uncertainty principle.

                                                                                                                                    (16 lectures)

Unit 5

Time dependent Schrodinger equation: Time dependent Schrodinger equation and dynamical evolution of a quantum state; Properties of Wave Function. Interpretation of Wave Function: Probability and probability current densities in three dimensions; Conditions for Physical Acceptability of Wave Functions.

(6 Lectures)

Unit 6

Quantum theory of hydrogen-like atoms: time independent Schrodinger equation in spherical polar coordinates; separation of variables for second order partial differential equation; angular momentum operator & quantum numbers; Radial wavefunctions from Frobenius method; shapes of the probability densities for ground and first excited states; Orbital angular momentum quantum numbers l and m; s, p, d shells.

(9 Lectures)

Recommended Books:

1.     Quantum Mechanics, B. H. Bransden and C. J. Joachain; 2nd Ed., Prentice Hall, 2000.

2.     A Text book of Quantum Mechanics, P.M. Mathews and K. Venkatesan, 2nd Ed.,2010, McGraw Hill.

3.     Quantum Mechanics for Scientists & Engineers, D.A.B. Miller, 2008, Cambridge University Press.

4.     Quantum Mechanics: Theory and Applications, (2019), (Extensively revised 6th Edition), Ajoy Ghatak and S. Lokanathan, Laxmi Publications, New Delhi.

5.     Introduction to Quantum Mechanics, D.J. Griffith, 2nd Ed. 2005, Pearson Education.

6.     Introduction to Quantum Mechanics, R. H. Dicke and J. P. Wittke, Addison-Wesley Publications, 1966.

7.     Quantum Mechanics, Leonard I. Schiff, 3rd Edn. 2010, Tata McGraw Hill.

8.     Quantum Mechanics, Robert Eisberg and Robert Resnick, 2ndEdn., 2002, Wiley.

9.     Quantum Mechanics: Concepts and Applications, 2nd Edition, Nouredine Zettili, A John Wiley and Sons, Ltd., Publication