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Quantum Mechanics (Theory) [1]

Paper Code: 
24DPHY712
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
Course Objectives:
This course will enable the students to-
• provide an understanding of the formalism and language of quantum mechanics.
• learn perturbation method to find out energy eigen states and wave functions for a system.
• understand the concepts of transition between stationary states, symmetries and angular momentum.
• apply quantum mechanical procedures for solving different types of problems.
• understand C.G. coefficients and time reversal symmetry.
 
Course Outcomes: 

Course Outcomes (COs):

 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

    Course Code

Course Title

 

 

 

24DPHY712

Quantum Mechanics

(Theory)

 

CO164: Demonstrate the ability to apply Hermitian operators to quantum-mechanical systems, analyze quantum states using Dirac's Bra and Ket notation, and understand the principles of eigenstates, eigenvalues, and degeneracy.

CO165: Apply approximation methods to study stationary states, analyze time-independent perturbations, and solve problems related to harmonic oscillators and degenerate perturbation theory.

CO166: Develop proficiency in analyzing two-state quantum systems, diagonalizing energy matrices, and solving time-independent perturbations in such systems .

CO167: Relate conservation laws with symmetries and convert various operators in coordinate and momentum representations.

CO168: Analyze the angular momentum operators and C.G. Coefficients and analyze quantum many body problems.

CO169: Contribute effectively in

course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Solving problems in tutorials, Demonstration. Power point Presentation

 

 

Learning activities for the students:

Self learning assignments, Effective questions, Seminar presentation.

Additional learning through online videos and MOOC courses

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

 

14.00
Unit I: 
I
I(a)  States, Amplitude and Operators: Hermitian operators and their properties, Unitary operators, Dirac’s Bra and Ket notation: Normalization and orthogonality conditions; Orthonormality; Eigen states and eigen values of an operator; Degeneracy.
States of a quantum mechanical system, Representation of quantum-mechanical states, Properties of quantum mechanical amplitudes, Operators and change of state, a complete set of basis states, product of linear operators.
I(b) Observables and Description of Quantum Systems:.
Process of measurement; Expectation values; Time dependence of quantum mechanical amplitudes; Observables with no classical analogue: spin; Dependence of quantum mechanical amplitude on position: the wave functions; Super position of amplitudes: interference.
 
10.00
Unit II: 
II
II(a)  Stationary States of a Quantum System: Hamiltonian matrix and the time evolution of  Quantum mechanical States; Hermiticity of the Hamiltonian matrix; 
II(b)  Approximation Methods for Stationary states; Time independent perturbation of a nondegenerate system; Harmonic Oscillator and simple matrix examples of time-independent perturbation, Degenerate Perturbation Theory.
10.00
Unit III: 
III
Hours) III(a)  Two State Systems: Energy eigen states of a two state system; Diagonalizing the energy matrix, Time independent perturbation of a two-state system, the perturbation solution: weak field and strong field cases; General description of a two-state system: Pauli matrices; Ammonia molecule as an example of two state system.
III(b)  Transition between Stationary States: Transitions in a two state system; Time dependent
perturbations: The Golden Rule, Adiabatic and Sudden Perturbation, Phase space, Energy width of quasi stationary states.
12.00
Unit IV: 
IV
IV(a) Symmetries: Compatible observables and constants of motion; Symmetry transformation and conservation laws; Invariance of the Hamiltonian; Invariance under space and time translations and space rotation and conservation of momentum, energy and angular momentum. Space inversion, Time Reversal.
IV(b) Coordinate and Momentum Representation: Coordinate representation of operators:
position, momentum and angular momentum, Time Dependence of expectation values, Components of
angular momentum operator in Cartesian and spherical polar coordinates, Commutation relations.
 
12.00
Unit V: 
V
V(a) Angular momentum : Angular momentum operators and their eigen values; Matrix representation of the angular momentum operators and their eigen states; Coordinate representation of the orbital angular momentum operators and their eigen states (Spherical Harmonics).
V(b) Composition of angular momenta; Clebsch-Gordon Coefficients; Recursion relations; Construction procedure; C.G. Coefficients for simple cases (j1 = ½ , j2 = ½ ;  j1=1, j2 = ½;  j1=1, j2=1), Irreducible spherical tensor operators,  Wigner-Eckart theorem.
Essential Readings: 
• “Quantum Mechanics - A modern approach “, Ashok Das and A.C. Melissinos ,Gordon and Breach Science Publishers (1990)
• “Quantum Mechanics“ L.I. Schiff, Mc Graw Hill Book company (1968)
• “Perspective of Quantum Mechanics” S.P. Kuila, New Central Book Agency(P) Ltd. London (2011)
• “Quantum Mechanics - Theory and Applications”, A. Ghatak and S. Lokanathan, V Edition, Mc Millan, India Ltd. (2010).
• “Quantum Mechanics; Concept and Application” N. Zettili (Wiley Publication).
• Modern Quantum Mechanics by J.J. Sakurai (Addison-Wesley, 1999).
 
References: 
• Quantum Physics (atoms, molecules…) R. Eisberg and R. Resnick (J. Wiley), 2005.
• “The principles of Quantum Mechanics”, P.A.M. Dirac, IV Edition, Ox Ford University Press (2008)
• “Quantum Mechanics”, E. Merzbecher, Third Edition, Wiley India (2012)
“Quantum Mechanics - Relativistic theory “, L.P. Landau and E.M. Lifshitz ,Pergamon Press.
• ”Modern Quantum Mechanics”, J. J. Sakurai , Pearson (1994)
• “A text book of Quantum Mechanics” P.M. Mathews & K. Venkatesan, Tata Mc Graw Hill, New Delhi IV Edition (2012).
• Quantum Mechanics”, John L. Powell & B. Crasemann, Addison Wesley (1963).
 
E-CONTENTS:
 
 
Academic Year: 
2024-2025 [4]

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Links:
[1] https://physics.iisuniv.ac.in/courses/subjects/quantum-mechanics-theory
[2] http://puccini.chimica.uniba.it/didattica/corsi/solid_state_chem/qm/Quantum_Mechanics_Thankappan.pdf 
[3] https://application.wiley-vch.de/books/sample/352740984X_c01.pdf 
[4] https://physics.iisuniv.ac.in/academic-year/2024-2025