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QUANTUM MECHANICS
Paper Code:
PHY123
Credits:
04
Contact Hours:
60.00
Max. Marks:
100.00
12.00
Unit I:
UNIT I
(a) Operator formalism in Quantum Mechanics: Hermitian operators and their properties, Unitary operator; Angular momentum; Components of angular momentum operator in Cartesian and spherical polar coordinates; Commutation relations.
Dirac’s Bra and Ket notation; Normalization and orthogonality conditions; Orthonormality; Eigen states and eigen values of an operator; Degeneracy;
(b) States, Amplitude and Operators: 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, Postulates, essential definitions and relations in Quantum mechanics.
12.00
Unit II:
UNIT II
(a) 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; Identical particles.
(b) 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; 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:
UNIT 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.
(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: Ehrenfest Theorem
12.00
Unit IV:
UNIT 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.
(b) Irreducible tensor operators; Product of tensor operators; Combination of operator and eigen state; Wigner-Eckart theorem; Space inversion;
12.00
Unit V:
UNIT 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).
(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).
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)
References:
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)
Academic Year:
