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Week Due |
exercises |
Lectures |
contact hours |
Topics List |
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1 |
2 |
2 |
4 |
Mathematical Supplement: Dirac delta function, Heaviside step function and Sign Function, Fourier and inverse Fourier integral transforms, Parseval’s theorem. |
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1 |
2 |
2 |
4 |
The origins of quantum theory: Overview on black body radiation, photoelectric effect and Compton effect. |
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1 |
2 |
2 |
4 |
Wave-Particle Duality: De Broglie’s hypothesis and the wave properties of matter, Propagation and spreading of wave packets, Concept of group velocity for wave packets, Free-particle propagator. |
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1 |
2 |
2 |
4 |
The wave function and Schrodinger equation: Time-dependent Schrodinger equation (TDSE), Dynamical variables and operators, Born’s interpretation of the wave function, Conservation of probability, Probability current density and continuity equation, The momentum-space wave function and its probabilistic interpretation. Expectation values. |
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2 |
4 |
4 |
8 |
Heisenberg Uncertainty Principle: The position-momentum uncertainty principle, Time-energy uncertainty relation and the meaning of the uncertainty in time, Ehrenfest’s theorem in one dimension, Linear operators and eigenvalue equations. |
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2 |
4 |
4 |
8 |
Separation of Variables for TDSE: Stationary-state solutions and their properties, Bound and unbound states, Orthonormalization of bound-state and unbound-state eigenfunctions, General solution of the TDSE for time-independent potentials, The interpretation and computation of the expansion coefficients in the general solution of the TDSE, Schrodinger equation in momentum space. |
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2 |
4 |
4 |
8 |
Hermitian operators: Definition and properties of Hermitian operators, Commutators and commutation relations, Algebra of commutators, Time development of expectation values and the constants of motion, The generalized uncertainty relation. |
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2 |
4 |
4 |
8 |
Illustrative Examples: Infinite well potential, Step potential, Barrier potential, Tunnelling effect, The Finite square well potential, The delta-function potential, Linear harmonic oscillator, Hermite polynomials and their properties, A particle in a potential box and degenerate states, The three-dimensional harmonic oscillator. |
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2 |
4 |
4 |
8 |
Angular momentum: Orbital angular momentum L in Cartesian and spherical coordinates, Commutators of angular momentum components, Eigenvalues and eigenfunctions of L2 and Lz , Spherical harmonics and their properties, Particle on a sphere and the rigid rotator, Quantum ring |
Learning Resources
|
Text Book |
|||
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Reference's name |
publisher |
Release |
Author |
|
2nd edition, 2000 |
Pearson Education |
B. H. Bransden and C. J. Joachain |
Quantum Mechanics |
|
Additional References |
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|
2004 |
Kluwer Academic Publishers |
A. Ghatak and S. Lokanathan |
Quantum Mechanics: Theory and Applications |
|
4th edition, 2002 |
Addison-Wesley |
R. Liboff |
Introductory Quantum Mechanics |
|
3rd edition, 2003 |
Wiley International edition |
S. Gasiorowicz |
Quantum Physics |