Week |
Subject |
Related Preparation |
1) |
Superposition principle. Normalization of finite function. Measurement in Quantum Mechanics. Expectation value. Uncertinity principle. |
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2) |
Wave packets. Standing waves. Wave packets and uncertainity principle. Motion of the wave packets. |
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3) |
Mathematical tools of Quantum Mechanics. Operators. Hermition adjoint. Projection operators. Commutator algebra. Uncertinity principle between two operators. Inverse and identical operators. Eigenvalues and eigenfunctions of operators. |
|
4) |
Dirac notation. Ket, Bra and definition of the operators in separated matrix presentation. Variation of the basic and unit transformations. Eigenvalue problem of matrix presentation. |
|
5) |
Definition of continuity principle. Notations of Momentum and position. Interrelations of momentum and position notations. Parity operators. |
|
6) |
Schrödinger equation. Stationary states. Time independent potential. Conservation of probability. Time dependent operators. Schrödinger equation and wave packets. Time dependency of expectation values. |
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7) |
Solution of one dimensional Schrödinger equation. Square well with finite depth. Infinite square well. Single step potential. Barrier problems. Tunneling in a large barrier. |
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8) |
Harmonic oscillator. Matrix presentation of various operators. Expectation values of various operators. |
|
9) |
Angular momentum. Orbital angular momentum. Matrix presentation of angular momentum. Geometric presentation of angular momentum. Schrödinger equation in spherical coordinates. Orbital and angular momentum operator. properties of spherical harmonics. |
|
10) |
Coulomb potential. General properties of radial wave for hydrogen atom. Complete Coulomb wavefunction. Hydrogen atom. Spherical symmetric solutions for hydrogen-like systems. Irreducible tensor operators. |
|
11) |
Time dependency of quantum states. Wave-packets states for free particle and dynamic particle. Energy-time uncertinity relation. |
|
12) |
Approximation methods for uniform states. Time-independent perturbation theory. Non-degenerate perturbation theory. |
|
13) |
Degenerate perturbation theory. Fine structure of hydrogen. Zeeman and Stark cases. Very fine splitting. High degrees in perturbation theory. |
|
14) |
Time-dependent perturbation theory. Adiabatic perturbation. Instant perturbation. |
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Course Notes / Textbooks: |
Quantum Mechanics. Non-relativistic theory by L.D.Landau and E. M. Liftshitz |
References: |
1.L.Schiff Quantum Mechanics McGraw-Hill,1964,
2.J.Sakurai Modern Quantum Mechanics. Addison-Wesley Publishing Company ,1994
3.A.Messiah Quantum Mechanics. Dover Publications, 1999
4.N.Zettili Quantum Mechanics. Wiley,2008
5.E.Merzbacher Quantum Mechanics. Wiley,1998
6. R.Shankar Principles 0f Quantum Mechanics. Kluwer, 1994
7.C.Cohen-Tannoudji, B.Diu, F.Laloe Quantum Mechanics v.1 and 2, Wiley,1997 |
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Program Outcomes |
Level of Contribution |
1) |
Ability to assimilate mathematic related concepts and associate these concepts with each other. |
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2) |
Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. |
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3) |
Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. |
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4) |
Ability to make individual and team work on issues related to working and social life. |
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5) |
Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. |
|
6) |
Ability to use mathematical knowledge in technology. |
|
7) |
To apply mathematical principles to real world problems. |
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8) |
Ability to use the approaches and knowledge of other disciplines in Mathematics. |
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9) |
Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. |
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10) |
To apply mathematical principles to real world problems. |
|
11) |
To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. |
|
12) |
To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. |
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