COURSE UNIT TITLE

: MODERN QUANTUM MECHANICS-II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5190 MODERN QUANTUM MECHANICS-II ELECTIVE 2 2 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR MUHAMMED DENIZ

Offered to

Nanoscience and Nanoengineering
Nanoscience and Nanoengineering
PHYSICS
PHYSICS
Nanoscience and Nanoengineering

Course Objective

This physics course offers a sophisticated view of quantum mechanics and its proper mathematical foundation. You will review the basics of wave mechanics and be introduced to the variational principle. You will learn about the technology of spin one-half states and spin operators and get an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. This course concludes by developing the bra-ket notation of Dirac.

To follow this course you will need some basic familiarity with quantum mechanics. You must have seen the Schrödinger equation and studied its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. You must be proficient in calculus and have some knowledge of linear algebra. This physics course covers Heisenberg s uncertainty principle and the concept of compatible operators. You will also learn about the Schrödinger and Heisenberg pictures of quantum mechanics and the coherent and squeezed states of the harmonic oscillator.

This course is offering a sophisticated view of quantum mechanics and its proper mathematical foundation. You will learn about angular momentum and its representations. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. Lastly, you will learn about the addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.

Learning Outcomes of the Course Unit

1   Basics of Wave Mechanics; Simple applications of the Variational Principle.
2   Spin one-half and spin operators; Linear algebra; Bra-ket notation.
3   Heisenberg uncertainty principle and compatible operators; The Schrödinger and Heisenberg pictures of quantum mechanics.
4   Representations of angular momentum; The central potential problem.
5   Addition of angular momentum; An algebraic approach to the hydrogen atom.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Wave Mechanics
2 Tutorial on Attractive 1-Dimensional Potential and Potentials with Delta-Functions
3 Wave Mechanics and Stern-Gerlach Experiment; Matrix Representaions for x and p
4 Spin One-half, Bras, Kets, and Operators; Tutorial on Index Manipulation
5 Linear Algebra: Vector Spaces and Operators; Tutorial on Matrix Representation
6 Linear Algebra: Vector Spaces and Operators (cont.)
7 Dirac's Bra and Ket Notation; Tutorial on Dirac Bra-Kets
8 MIDTERM
9 Uncertainty Principle and Compatible Observables; Problem Solving Tutorial: Saturating the Uncertainty Inequality
10 Quantum Dynamics
11 Problem Solving Tutorial: 4 ways to do a computation; Tutorial: Virial Theorem in Classical Physics; Tutorial: Virial Theorem and the Hydrogen Atom
12 Photon States and Two State Systems
13 Angular Momentum; Tutorial: Representations of Angular Momentum
14 Addition of Angular Momentum

Recomended or Required Reading

Textbook(s):
1. J.J. Sakurai, Modern Quantum Mechanics,
2. David Griffiths, Introduction to Quantum Mechanics.

Supplementary Book(s):
1. Principles of Quantum Mechanics, Shankar.
2. Quantum Mechanics: Concepts and Applications, Zettili

Planned Learning Activities and Teaching Methods

1. Method of Expression
2. Question & Answer Techniques
3. Discussion
4. Homework assignments

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.25 + ASG * 0.25 + FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG * 0.25 + FIN * 0.50


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

1. Midterm exams and assignments are taken as the achievements of students for the semester.
2. Final exam will be added to the success of the study of midterms and assignments, thereby the student's success will be determined.

Language of Instruction

English

Course Policies and Rules

1. Policy and Rules Concerning the course: 70% of the participation of classes is mandatory.
2. Students who do not participate in Midterm exams and not do the assignments regularly are not allowed entering the final exam

Contact Details for the Lecturer(s)

muhammed.deniz@deu.edu.tr

Office Hours

Monday at 09: 30 - 11: 30

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 2 26
Tutorials 13 2 26
Preparations before/after weekly lectures 13 5 65
Preparation for midterm exam 1 5 5
Preparation for final exam 1 5 5
Preparation for quiz etc. 6 5 30
Preparing assignments 4 5 20
Final 1 3 3
Midterm 1 3 3
Quiz etc. 6 3 18
TOTAL WORKLOAD (hours) 201

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.15544
LO.25544
LO.35544
LO.4554455
LO.55555455

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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