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Week Due |
Exercises |
Lectures |
contact hours |
Topics List |
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Central Potentials: Separation of the Schrödinger equation in spherical coordinates, A particle in spherical well potential, The harmonic oscillator in spherical coordinates, The Hydrogen atom, Associated Laguerre polynomials and the radial Schrödinger equation, Energy quantization of the Hydrogen atom and degeneracy of the bound states. |
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Mathematical Foundations of QM: Dirac notation, The bra and ket algebra, The position and momentum representations of the ket- and bra-vectors, Hilbert Space and State Vectors, Dimension and Basis of Hilbert Space, Expansion of state vectors in terms of orthonormal basis and the calculation of the expansion coefficients, Projection operators, Completeness of a set of eigenfunctions, Completeness relation, Commuting observables and the common eigenfunctions. |
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Postulates of Quantum Mechanics. |
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Operator methods in QM: Operator approach to the harmonic oscillator problem, Calculating expectation values of the oscillator observables using ladder operators, Solving the eigenvalue equation of the angular momentum squared by the operator method. |
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Matrix Mechanics: Linear transformation on Hilbert space, Matrix representation of state vectors and linear operators, Expectation values in matrix form. Hermitian and Unitary matrices, Trace of a linear operator, Change of bases and unitary transformations, Matrix representation of eigenvalue equations, Diagonalization of matrices and the calculation of eigenvalues and eigenvectors. |
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Application of Matrix Mechanics: Calculating matrix elements for the harmonic oscillator observables using the ladder operators, Matrix representation of angular momentum and its ladder operators , The components of the angular momentum in matrix form. Spin angular momentum and the theory of spin, Spin-1/2 and the Pauli matrices, Spin-1/2 eigenvectors, Addition of two angular momenta. |
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Approximation Methods: The time-independent perturbation theory, The first and second order corrections for the nondegenerate states, A charged harmonic oscillator in an electric field, Stark effect in the Hydrogen atom, Zeeman effect, Variational Method. |
Learning Resources
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Text Book |
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Reference's name |
publisher |
Release |
Author |
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Quantum Mechanics |
Prentice Hall |
2nd Edition |
Bransden and Joachain |
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Quantum Mechanics |
Wiley |
2nd Edition |
N. Zettili |
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Additional References |
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Introductory Quantum Mechanics |
NJ: Prentice Hall |
4th Edition |
R.Liboff |
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Introduction to Quantum Mechanics |
W H Freeman & CoW H Freeman & Co |
2nd Edition |
Bransden B. H., and Joachain C. J., |