ICFAI University Tripura

Course Handout

B.Sc Physics 2nd year Semester I: 2020 -2021

 

 

Course No

Course Title

L

T

P

U

PHY214T

Quantum Mechanics I

3

1

0

4

Course Instructor: Dr. Camelia Das

Text Books:

1.      T1: Quantum Mechanics: concepts and applications, Nouredine Zettili, Second edition Wiley

2.      T2: Perspective of Quantum Mechanics, S. P. Kuila, New Central Book Agency (P) Ltd.

Reference Books:

1.      R1: Introduction to Quantum Mechanics, David J. Griffiths, Second Edition, Pearson Education.

Learning objective

Newtonian mechanics was found to be inadequate in the early years of this century- it’s all right in “everyday life”, but for objects moving at high speeds (near speed of light) it is incorrect, and must be replaced by special relativity (introduced by Einstein in 1905); for the objects that are extremely small (near the size of atom) it fails for different reasons, and is superseded by quantum mechanics (developed by Bohr, Schrödinger, Heisenburg, and many others). For objects that are both very fast and very small (as in common in modern physics), a mechanics that combines relativity and quantum principles is in order: this relativistic quantum mechanics is known as quantum field theory.

Learning outcome

Quantum mechanics-I (PHY214T) offers a systematic introduction to fundamental non-relativistic quantum mechanics. This course introduces the origin of quantum mechanics (black body radiation curve), wave aspects of particles, matter waves, classical and quantum view of particles and waves, concept of wave packets, mathematical tool of quantum mechanics (operators, wave function, eigen value equation, expectation value of dynamical variable), probabilistic interpretation of wave function, stationary states, normalization and orthogonality of wave function, Schrödinger equation with simple solution of step potentials.

The student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

 

The student has gained knowledge about

1.      basic non-relativistic quantum mechanics

2.      Wave aspect of particles (wave function and its probabilistic interpretations)

3.      the time-dependent and time-independent Schrödinger equation for simple potentials

Skills

 

The student is able to

1.      apply principles of quantum mechanics to calculate observables on known wave functions

2.      solve time-dependent and time-independent Schrödinger equation for simple potentials

General competence

 

The student has gained

*      knowledge about fundamental quantum mechanical processes in nature

*      experience using mathematical tools to construct approximate quantum mechanical models

 

Lecture-wise plan:

Lecture Nos.

Learning Objective

Topics to be covered

Chap./Sec. (Text Book)

1 – 5

Basic Understanding origin of quantum physics

Historical .Note, Particle Aspect of Radiation: Black Body Radiation, Photoelectric Effect, Compton Effect, Pair Production

T1: 1.1 - 1.2

6- 8

To understand the concept of wave aspects of particles:

Broglie’s Hypothesis (Matter waves), Matter waves for Macroscopic Objects

T1: 1.3

9- 13

To study the particles versus Wave nature

Classical Views on Particles and Waves, Quantum Views on Particles and Waves, Wave Particle Duality, Principle of Linear Superposition.

T1: 1.4

13-15

To understand in-deterministic nature of the microphysical world

Heisenberg’s Uncertainty Principle, Probabilistic Interpretation

T1: 1.5

16 - 20

To understand the basic concept of atomic transition and spectroscopy and quantization rules

Rutherford Planetary Model of Atom, Bohr Model of the Hydrogen Atom.

T1: 1.6 – 1.7

21 - 23

To study the concept of wave packets

Localized Wave Packets, Wave packets and the Uncertainty relations, Motion of Wave Packets.

T1: 1.8

24 - 26

To study the mathematical tools of quantum mechanics (The Hilbert Space and Wave Functions)

The Linear Vector Space, The Hilbert Space, Dimensions and basis of vector space, Wave Functions.

T1: 2.1 – 2.2

27 - 35

To study the mathematical tools of quantum mechanics (Dirac Notation and Operators)

Dirac Notation, Hermitian Adjoint, Projection Operators, Commutator Algebra, Uncertainty Relation between Two Operators, Function Operators, Inverse and Unitary Operators, Eigen values and Eigen vectors of an Operator.

T1: 2.3 – 2.4

36 - 41

To understand the representation of discrete continuous bases

Matrix representation of Kets, Bras and Operators, Prepresentation of Continioud Bases: Position Representation, Momentum Representations, Connecting the Position and Momentum Representations, Parity Operator, Matrix and Wave Mechanics

T1: 2.5 – 2.7

42 - 47

To understand the postulates of quantum mechanics

The Basic postulates of quantum Mechanics, The State of a System: Probability Density, Superposition Principle, Observables and Operators, Measurement in Quantum Mechanics: How Measurements Disturb Systems, Expectation Values, Complete set of Commutating Operators, Measurement and the Uncertainty Relations.

T1: 3.1 – 3.5

47 - 52

Time evolution of System’s State: Time Evolution Operator, Stationary States: Time Independent Potentials, Schrödinger Equation and Wave Packets, The Conservation of Probability, Time evolution of Expectation Values, Poisson Brackets and Commutators, The Ehrenfest Theorem.

T1: 3.6 – 3.8

53 - 60

One Dimensional Problem

Properties of one-dimensional motion, Free particle: Continuous states, Potential Step, Harmonic Oscillator: Energy Eigen values, Energy Eigen vectors, Energy states in position Space, Matrix representation of Various Operators.

T1: 4.2 – 4.3 & 4.8

 

Evaluation Scheme:

Component

Weightage(%)

Internal I (assignment/presentation)

25

Mid-term

20

Internal II (assignment/presentation)

25

Comprehensive

30

 

  1. Chamber Consultation Hour: Course Instructor will announce in the class.

(During the Chamber Consultation Hours, the students can consult in Faculty’s chamber without prior appointment.)

2.      Attendance Policy: A Student must normally maintain a minimum of 75% attendance in the course without which he/she shall be disqualified from appearing in the respective examination.

3.      Make-up Policy: A student, who misses any component of evaluation for genuine reasons, must immediately approach the instructor with a request for make-up examination stating reasons. The decision of the instructor in all matters of make-up shall be final.

                                                                                                Dr. Camelia Das

Date:   11.09.2020                                                                              C/I