COURSE UNIT TITLE

: MODERN QUANTUM MECHANICS-I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 5143 MODERN QUANTUM MECHANICS-I 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

In this quantum physics course you will learn the basics of quantum mechanics. We begin with de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrödinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest's theorem, and uncertainty relations.

In this quantum physics course you will acquire concrete knowledge of quantum mechanics by learning to solve the Schrödinger equation for important classes of one-dimensional potentials. We study the associated energy eigenstates and bound states. The harmonic oscillator is solved using the differential equation as well as algebraically, using creation and annihilation operators.

In this quantum physics course you will learn the basic concepts of scattering phase-shifts, time delays, Levinson's theorem, and resonances in the simple context of one-dimensional problems. We then turn to the study of angular momentum and the motion of particles in three-dimensional central potentials. We learn about the radial equation and study the case of the hydrogen atom in detail.

Learning Outcomes of the Course Unit

1   Learning the wavefunction and its probability interpretation; the Schrödinger equation.
2   Learning inner products and Hermitian operators; time-evolution of wave-packets; Ehrenfest's theorem and uncertainty relations.
3   Learning solutions of the Schrodinger equation for one-dimensional potentials: the square well and the harmonic oscillator. Learning algebraic solution of the harmonic oscillator.
4   Basics of quantum scattering in one dimension; Learning basic concept of angular momentum in Quantum Mechanics.
5   Learning three-dimensional central potentials; Solution of 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 Overview of quantum mechanics, Interaction-free measurements
2 Photoelectric effect, Compton scattering, de Broglie wavelength
3 de Broglie matter waves, Group velocity and stationary phase, Free particle waves
4 Momentum operator, Schrödinger equation, Interpretation of the wavefunction; Probability density and current, Hermitian conjugation
5 Wavepackets and uncertainty, Time evolution and shape change; Uncovering momentum space, Expectation values and their time dependence
6 Observables, Hermitian operators, measurement and uncertainty; Stationary states
7 Infinite and finite square wells, Properties of bound eigenstates; Properties of 1D energy eigenstates, Qualitative properties of wavefunctions
8 MIDTERM
9 Delta function potential; Simple Harmonic Oscillator, Creation and annihilation operators
10 Simple Harmonic Oscillator II; Scattering states and step potential, Reflection and transmission coefficients, Phase shift, wavepackets and time delay
11 Central potentials and angular momentum; Legendre equation, Radial equation, Hydrogen atom 2-body problem
12 Hydrogen atom (ctd), differential equation, series solution and quantum numbers
13 Spectrum for hydrogen, Virial theorem, circular orbits and eccentricity, Degeneracies
14 The simplest quantum system and emergent angular momentum; de Broglie Waves

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 quiz etc. 6 5 30
Preparing assignments 4 5 20
Preparation for final exam 1 5 5
Preparation for midterm exam 1 5 5
Midterm 1 3 3
Final 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.10
LO.15555453542
LO.25555453542
LO.35555453542
LO.45555453542
LO.55555453542

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

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