FİZ6039 Quantum Mechanics IIBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
MATHEMATICS (TURKISH, PHD)
PhD TR-NQF-HE: Level 8 QF-EHEA: Third Cycle EQF-LLL: Level 8

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
FİZ6039 Quantum Mechanics II Fall 3 0 3 12
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Dr. Öğr. Üyesi ÖMER POLAT
Recommended Optional Program Components: None
Course Objectives: To give basic knowledge about the theoretical foundation of quantum mechanics of many particles system.

Learning Outcomes

The students who have succeeded in this course;
Upon successful completion of this course, students:

1-apply quantum mechanics of many particles system.

2-explain the macroscopic behaviour of matter.

3-emphasize the importance of quantum mechanics in modern physics and chemistry

4-ability to use the approaches and knowledge of other disciplines

Course Content

In this course,
The Wentzel – Kramers – Brillouin approximation method, Tunneling through a Potential Barrier,Spin Angular Momentum, Pauli Exclusion Principle,Spin – orbit forces,Theory of Radiation,Elements of Relativistic Quantum mechanics will be taught.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) The Wentzel – Kramers – Brillouin approximation method. One dimension WKB solutions. Conditions for the validity of the WKB approximation. Turning Point and connection formulas
2) Bound States for Potential wells with No (One, Two) Rigid Walls. Energy levels of a potential well. The "Classical" region. Tunneling through a Potential Barrier.
3) Spin Angular Momentum. Quantum Mechanical Description of the Spin. The Spin Operator, Pauli Matrices, and Spin Angular Momentum Eigenvalues. Quantum Dynamics of a Spin System. Density matrix and Spin Polarization
4) Spin and Rotations. Properties of the Rotation Operator. Representation of the Rotation Operator. Euler Rotations. Spinors
5) The Addition of Angular Momenta. Addition of Two Angular Momenta: General Formalism. Calculation of the Clebsch – Gordan Coefficients. Coupling of Orbital and Spin Angular Momenta.
6) Addition of More than two Angular Momenta. Tensor operators and the Wigner – Eckart Theorem for Spherical Tensor Operators. Reflection Symmetry, Parity, and Time Reversal. Isospin. Midterm exam I
7) Identical Particles. Many Particle Systems. Symmetrization Postulate. Constructing Symmetric and Antisymmetric Wave Functions.
8) Exchange Degeneracy. Systems of Identical Noninteracting Particles. The Pauli Exclusion Principle. Exclusion Principle and the Periodic Table.
9) Quantum dynamics of Identical Particles. Angular Momentum of System of Identical particles. Angular Momentum and Spin One Half Boson Operators. Helium Atom. Ground State of the helium Atom. First order perturbation theory in many Body Systems. The Hartree – Fock Method
10) The calculus of Variations in Quantum Mechanics. The Rayleigh – Ritz Trial Function. Variation method for Bound States. Variational Form of the eigenvalue problem. Variational calculation of discrete levels. A simple example: The Hydrogen Atom and Harmonic Oscillator. Application to the calculation of excited levels.
11) Spin – orbit forces. LS and jj coupling. The atom in LS coupling. Splitting due to spin – orbital coupling. The normal and anomalous Zeeman Effect. Theory of molecules in adiabatic Approximation. Hydrogen molecule Midterm exam II
12) Field Quantization. Theory of Radiation. Energy: Momentum and Angular Momentum of the radiation Field. Normal Vibrations. Quantization of the Free Field. Lagrangian of the field. Plane Waves. Photons. Polarization. Emission of a photon by an atom. Dipole emission.
13) Scattering. The Cross Section. The Scattering of a Wave Packet. Scattering Amplitude and Differential Cross Section of Spinless particles. Green’s Functions in Scattering Theory. The Born Approximation. Partial Wave and Phase Shifts. Determination of the Phase Shifts and Scattering Resonances. Phase Shifts and Green’s Functions. Scattering in a Coulomb Field. Partial Wave analysis for Elastic and Inelastic Scattering.
14) Elements of Relativistic Quantum mechanics. The Dirac and Klein – Gordon equations. Dirac theory in the Heisenberg picture. Dirac theory in the Schrödinger Picture and the Nonrelativistic Limit. .Negative Energy solution and positron theory.

Sources

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

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Quizzes 4 % 10
Homework Assignments 4 % 20
Midterms 1 % 30
Final 1 % 40
Total % 100
PERCENTAGE OF SEMESTER WORK % 60
PERCENTAGE OF FINAL WORK % 40
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 6 84
Homework Assignments 4 8 32
Quizzes 4 5 20
Midterms 1 10 10
Final 1 12 12
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution