Quantum Mechanics II (Theory)

Paper Code: 
CPHY 712
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

Course Objectives:

This course will enable the students to

  1. To provide an understanding of the formalism and language of quantum mechanics.
  2. To learn perturbation method to find out energy eigen states and wave functions for a system.
  3. To understand the concepts of transition between stationary states, symmetries and angular momentum.
  4. To apply quantum mechanical procedures for solving different types of problems.
  5. To understand C.G. coefficients and time reversal symmetry.

 

Course Outcomes (COs):

 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

PAPER CODE

Paper Title

CPHY 712

Quantum Mechanics II

(Theory)

 

The students will be able to:

 

CO141: expand the knowledge of quantum theory formulation through Schrodinger equation and Heisenberg’s matrix mechanics after an exposition of inadequacies of classical mechanics in explaining microscopic phenomena.

 

CO142: learn about new Dirac specific notation such as bra and ket formalism and apply this notation to formulate the various problems in quantum mechanics and find energy eigen values through diagonalizes the matrix in simple cases.

 

CO143: interpret the wave function of quantum particle and probabilistic nature of its location and subtler points of quantum phenomena.

 

CO144: understanding the basic concept of perturbation theory, level splitting and radiative transitions and theit application to physical situations.

 

CO145: develop a knowledge and understanding of the relation between conservation laws and symmetries.

 

CO146: learn about angular momentum operators and C.G. Coefficients and analyze quantum many body problems.

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

 

CONTENTS

 

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 an nondegenerate system; Harmonic Oscillator and simple matrix examples of time independent perturbation, Degenerate Perturbation Theory.
10.00
Unit III: 
III
 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.
 
14.00
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: 
1. “Quantum Mechanics - A modern approach “, Ashok Das and A.C. Melissinos ,Gordon and Breach Science Publishers (1990)
2. “Quantum Mechanics“ L.I. Schiff, Mc Graw Hill Book company (1968)
3. “Perspective of Quantum Mechanics” S.P. Kuila, New Central Book Agency(P) Ltd. London (2011)
4. “Quantum Mechanics - Theory and Applications”, A. Ghatak and S. Lokanathan, V Edition, Mc Millan, India Ltd. (2010).
5. “Quantum Mechanics; Concept and Application” N. Zettili (Wiley Publication).
6. Modern Quantum Mechanics by J.J. Sakurai (Addison-Wesley, 1999).
References: 
1. Quantum Physics (atoms, molecules…) R. Eisberg and R. Resnick (J. Wiley), 2005.
2. “The principles of Quantum Mechanics”, P.A.M. Dirac, IV Edition, Ox Ford University Press (2008)
3. “Quantum Mechanics”, E. Merzbecher, Third Edition, Wiley India (2012)
“Quantum Mechanics - Relativistic theory “, L.P. Landau and E.M. Lifshitz ,Pergamon Press.
4. ”Modern Quantum Mechanics”, J. J. Sakurai , Pearson (1994)
5. “A text book of Quantum Mechanics” P.M. Mathews & K. Venkatesan, Tata Mc Graw Hill, New Delhi IV Edition (2012).
6. Quantum Mechanics”, John L. Powell & B. Crasemann, Addison Wesley (1963).
 
E-CONTENTS:
1. Quantum Mechanics An Introduction by Walter Grenier (Third ed., 1994, Springer).
2. Relativistics Quantum Mechanics -Bjorken & Drell (Mc Graw hill)
3. Quantum mechanics-Thankpapn V.K.(Wiley Eastern ltd. New Delhi). http://puccini.chimica.uniba.it/didattica/corsi/solid_state_chem/qm/Quan...
4. Elements of Advance Quantum Theory- J.M. Ziman (Cambridge University Press).
 
 
 
 
 
Academic Year: 
2023-2024
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