Quantum Mechanics I (Theory)

Paper Code: 
CPHY 611
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

Course Objectives:

This course will enable the students to develop the basic knowledge of quantum mechanics and its application to various problems. It also deals with the techniques of wave mechanics like Schrödinger equation and its solution, angular momentum and spin. The student develops the understanding of quantum nature of e.m. radiations or light and wave nature associated with microscopic particles, the notion of quantum states, operators etc. 

Course

Learning outcome

(at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

CPHY 611

Quantum Mechanics I

(Theory)

The students will be able to –

 

CO104:  Interpret different types  of electromagnetic radiations.

 

 

CO105: Demonstrate the use  of Quantum mechanical operators.

 

CO106: Solve Schrodinger equations for a number of problems.

 

 

CO107: Apply Schrödinger equation to solve problems using   Boundary condition and continuity condition, Simple harmonic oscillator and Rigid rotator.

 

CO108: Acquire the knowledge of Angular momentum operators and their commutation relations.

 

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Power point presentation,  Problem Solving in tutorials

Learning activities for the students:

Self learning assignments, Effective questions, Seminar presentation, Solving numerical

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

12.00
Unit I: 
I
Introduction to Wave Mechanics:               
Electromagnetic Radiation, Black Body Radiation, Planck’ Law of Radiation, Photoelectric Effect, Compton Effect.
Schrodinger equation:
Wave function and its interpretation, Schrödinger time dependent and time independent one-dimensional equation, three-dimensional  Schrödinger wave equation, probability current density, physical meaning of  ψ, conditions to be satisfied by  ψ.
 
   
12.00
Unit II: 
II
Operator formulation in Quantum mechanics:                                                   
Operators, algebra of operators, commutative property, linear operators, Commutator operator, eigen values and eigen functions, operators for momentum, K.E., Hamiltonian, total energy and angular momentum, Fundamental postulates of Q.M.
Hermitian operators, orthonormality, degeneracy, Commutation relations, Ehrenfest’s theorem, Bohr’s principle of complementarity, principle of superposition.
 
 
12.00
Unit III: 
III
Simple solutions of Schrödinger equation:                                                            
Boundary  and continuity conditions on the wave function. Particle in one dimensional box, eigen function and eigen values, discrete energy levels, generalization to 3-D and degeneracy of levels
 
Boundary value problems:
Step potential, Penetration through rectangular barrier, calculation of reflection and transmission coefficients. Quantum mechanical  tunneling. Square well potential problem, reflection and transmission coefficient and resonant scattering.
12.00
Unit IV: 
IV
Simple harmonic oscillator (1-D Case): Schrödinger equation and its solutions, eigen function, energy eigen values. Zero point energy, parity, symmetric and anti-symmetric wave functions with graphical representation. Rigid rotator: Schrodinger equation and its solution.
 
 
 
12.00
Unit V: 
V

Angular Momentum: Introduction: orbital angular momentum, Operators for its Cartesian components, commutation relations, mutual as well as with L2 ,L+ and L- operators , their interpretation as step operators, eigen values of Lz, Total angular momentum operators, commutation relations obeyed by the components of generalized momentum operator. Commutation relation of  Jz with J+ and J- , J+ and J- ,commutation relation of J2 with J+ and J-.

Essential Readings: 
1. “Quantum Mechanics” L.L. Schiff, Tata Mc Graw Hill.
2. “Quantum Mechanics”, Chatwal and Anand, Himalaya Publishing House.
3. “Quantum Mechanics”, H. C. Verma, TBS Publishing House.
4. “Quantum Mechanics Concepts and Application”, Nouredine Zettili, WILEY Publishing House.
References: 
 
1. “Introduction to Modern Physics”,H.S. Mani and G.K. Mehta, East West Press Pvt. Ltd., New Delhi.
2. “Quantum Mechanics”, S.P. Singh, M.K. Bagde and Kamal Singh,S. Chand & Co.
3. “Quantum Mechanics”, A Listair, I M Rac, ELBS (low price edition).
4. “Quantum Mechanics”, S.N.Biswas, Books & Allied,Calcutta (P) Ltd.
5. “Perspectives of Modern physics”, A.Beiser, Mc Graw Hill.
6. “Problems on Quantum Mechanics”, Dr. S.L.Kakani, Arihant Publishing House.
 
Academic Year: 
2023-2024
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