APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
FİZ5037 | Quantum Mechanics I | Spring | 3 | 0 | 3 | 12 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Language of instruction: | Turkish |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. MUHAMMED AÇIKGÖZ |
Recommended Optional Program Components: | None |
Course Objectives: | Giving the principles of Quantum Mechanics and using Mathematics as an effective tool in solving of the Quantum Mechanics problems |
The students who have succeeded in this course; Using the principles of Quantum Mechanics as an effective tool in problem solutions. Integration to the recent scientific and technological developments. To comprehend the properties of the matter and the nature from the point of view of Quantum Mechanics I. |
In this course, the principles of Quantum Mechanics will be given and using Mathematics as an effective tool in solving of the Quantum Mechanics problems will be thought. |
Week | Subject | Related Preparation |
1) | Superposition principle. Normalization of finite function. Measurement in Quantum Mechanics. Expectation value. Uncertinity principle. | |
2) | Wave packets. Standing waves. Wave packets and uncertainity principle. Motion of the wave packets. | |
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. | |
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. | |
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. |
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 |
Semester Requirements | Number of Activities | Level of Contribution |
Homework Assignments | 5 | % 20 |
Midterms | 1 | % 40 |
Final | 1 | % 40 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 4 | 56 |
Homework Assignments | 5 | 10 | 50 |
Midterms | 1 | 22 | 22 |
Final | 1 | 30 | 30 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | 3 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 3 |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 3 |
4) | Ability to make individual and team work on issues related to working and social life. | 3 |
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. | 3 |
7) | To apply mathematical principles to real world problems. | |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 3 |
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. | 3 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | |
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, |