QUANTUM MECHANICS

Paper Code: 
PHY 123
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

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 outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

PHY 123

Quantum Mechanics

(Theory)

The students will be able to –

CO 11: Develop 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.

 

CO 12: Learn bra and ket formalism due to Dirac and apply the same to various problems

 

CO 13: Diagonalize the matrix and find energy eigen values in simple cases.

 

CO 14: Interpret  wave function of quantum particle and probabilistic nature of its location and subtler points of quantum phenomena.

 

CO 15: Develop a knowledge and understanding of perturbation theory, level splitting, and radiative transitions.

 

CO 16: Learn about time dependent perturbations and significance of Fermi golden role

 

CO 17: Develop a knowledge and understanding of the relation between conservation laws and symmetries.

 

CO 18: Learn about angular momentum operators and C.G. Coefficients.

 

CO 19: 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

 

12.00
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.
 
12.00
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; Time independent perturbation of an arbitrary system; Harmonic Oscillator and simple matrix examples of time independent perturbation;
 
II(b) 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. 
 
12.00
Unit III: 
III
III(a) Transition between Stationary States: Transitions in a two state system; Time dependent perturbations: The Golden Rule; Phase space, Emission and absorption of radiation; Induced dipole transition and spontaneous emission of radiation energy; Energy width of quasi stationary states.
 
III(b) The co-ordinate Representation: Compatible observables; Quantum conditions and uncertainty relation; Coordinate representation of operators: position, momentum and angular momentum; Time dependence of expectation values.
 
10.00
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) Angular momentum; 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)
 
 
 

BOOKS RECOMMENDED

  • “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)
  • “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)

 

References: 
 

 

Academic Year: 
2020-2021
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