Coming soon
Quantum Mechanics
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 and apply quantum mechanical procedures for solving different types of problems.
· understand C.G. coefficients and time reversal symmetry.
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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24PHY 123 |
Quantum Mechanics (Theory)
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CO13: 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 CO14: Apply approximation methods to study stationary states, analyze time-independent perturbations, and solve problems related to harmonic oscillators and degenerate perturbation theory CO15: Develop proficiency in analyzing two-state quantum systems, diagonalizing energy matrices, and solving time-independent perturbations in such systems CO16: Relate conservation laws with symmetries and convert various operators in coordinate and momentum representations. CO17: Analyze the angular momentum operators and C.G. Coefficients and analyze quantum many body problems. CO18: Contribute effectively in course-specific interaction.
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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 |
I(a) Hermitian operators and their properties, Unitary operators, Dirac’s Bra and Ket notation: Normalization and orthogonality conditions; Orthnormality; 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) 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.
II(a) Hamiltonian matrix and the time evolution of Quantum mechanical States; Hermiticity of the Hamiltonian matrix;
II(b)Time independent perturbation of an nondegenerate system; Harmonic Oscillator and simple matrix. examples of time independent perturbation, Degenerate Perturbation Theory.
III(a) 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) Transitions in a two state system; Time dependent perturbations: The Golden Rule, Adiabatic and Sudden Perturbation, Phase space, Energy width of quasi stationary states.
IV(a) 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 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.
V(a) 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.
- “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).
- 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: http://puccini.chimica.uniba.it/didattica/corsi/solid_state_chem/qm/Quantum_Mechanics_Thankappan.pdf
https://application.wiley-vch.de/books/sample/352740984X_c01.pdf
