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QUANTUM MECHANICS
- To provide an understanding of the formalism and language of quantum mechanics.
- To learn perturbation method to find out energy eigen states and wave functions for a system.
- To understand the concepts of transition between stationary states, symmetries and angular momentum.
- To apply quantum mechanical procedures for solving different types of problems.
- To understand C.G. coefficients and time reversal symmetry.
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PHY 123 |
Quantum Mechanics |
After the successful completion of the course, 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.
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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) 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.
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.
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.
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.
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.
- “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)
1.“The principles of Quantum Mechanics”, P.A.M. Dirac,. IV Edition, Ox Ford University Press (2008)
2 “Quantum Mechanics”, E. Merzbecher, Third Edition, Wiley India (2012)
3 “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)
