COURSE UNIT TITLE

: QUANTUM MECHANICS I

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
PHY 3903 QUANTUM MECHANICS I COMPULSORY 4 2 0 7

Offered By

Physics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR AYLIN YILDIZ TUNALI

Offered to

Physics

Course Objective

The aim of the course is to understand the principles and concepts of quantum mechanics, such as the Schrödinger equation, the wave function and its statistical interpretation, the uncertainty principle, stationary and non-stationary states, operator, eigenfunction, eigenvalue, time evolution of solutions, expectation values, associated probabilities, significance of measurements and uncertainties. Quantum mechanical interpretation of concepts such as angular momentum, and spin will be given, as well as total angular momentum will be discussed for quantum mechanical systems. Also the course creates mathematical background and to gains students an experience in solution of basic quantum mechanical problems. The materials and skills learned in this course provides a basis for further study of quantum mechanics.

Learning Outcomes of the Course Unit

1   To be able to discuss the fundamental principles of quantum mechanics, and gain a thorough comprehension of the concept of quantum mechanical wave function and its properties.
2   To be able to calculate the expectation values of physical observables, and to give physical interpretation to the uncertainty relations.
3   To be able to obtain eigenvalues and eigenstates using algebraic methods for a quantum system.
4   To be able to solve the Schrödinger equation on your own for simple 3-dimensional and 1-dimensional systems such as free particle, infinite square well, harmonic oscillator, finite square well, step potential, potential barrier both analytically and by using robust numerical methods.
5   Using these solutions to calculate time evolution of physical observables, associated probabilities, expectation values, and uncertainties, as well as to give concise physical interpretations and reasoning underlying the mathematical results.
6   To have mastered the concepts of angular momentum and spin, as well as the rules for quantisation and addition of these.
7   To be able to solve the angular and radial part of Schrödinger equation in spherical coordinates for hydrogen and similar atoms and to calculate the expectation values of observable quantities using these results.
8   To have knowledge about matrix formulation of quantum mechanics including spin and to understand the relation between the wave and the matrix mechanics.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 The requirement of Quantum Mechanics: A brief historical development. Blackbody radiation, heat capacity of solids, phonon momentum and Compton scattering of light, Bohr atomic theory. Wave character of massive particles, electron diffraction, de Broglie hypothesis. Heisenberg uncertainty principle.
2 Operators and eigenfunctions and eigenvalues of an operator. Hilbert space. Hermitian operators and properties of Hermitian operators.
3 Orthonormal functions. Commutation relations between operators. Uncertainty principle, a complete set of commuting observables.
4 Postulates of quantum mechanics. Schrödinger wave function and time evolution of wave function. Wave function and its statistical interpretation. Expectation values.
5 Time variation of expected values. Stationary states. Special operators: parity operator, projection operator. The law of conservation of energy, linear and angular momentum. Conservation of parity.
6 Solution of Shrödinger equation in one dimension, continuity conditions. Infinite square well problem. The finite potential well scattering problem.
7 One dimensional step potential, potential barrier and quantum tunelling.
8 MIDTERM EXAM
9 Eigenvalues and eigenfunctios of Harmonic oscillator. Rising and lowering operators (known as ladder operators).
10 Basic matrix algebra. Unitary and similarity transformations in quantum mechanics. Matrix representations of linear operators. Angular momentum and Pauli spin matrices.
11 Orbital angular momentum operators, eigenfunctions and eigenvalues.
12 Addition of angular momenta, total angular momentum of two or more electrons. Clebsch-Gordan coefficients.
13 Three dimensional solutions of Schrödinger wave function in both cartesian and spherical coordinates for free particle.
14 Schrödinger equation for two particle systems. Solution of Radial part for Hydrojen atom. Eigenfunctions and eigenvalues of Hydrogen atom.

Recomended or Required Reading

1) Principles of Quantum Mechanics, Ramamurti Shankar, Plenum Press, 2011.
2) Intoduction to Quantum Mechanics, David J. Griffiths, Benjamin Cummings, 2004.
3) Kuantum Mekaniği: Temel Kavramlar ve Uygulamaları, Tekin Dereli, Abdullah Verçin, ODTÜ Geliştirme Vakfı Yayıncılık, 2014.
4) Introductory to Quantum Mechanics, Richard L. Liboff, Addison-Wesley, 2003.
5) Quantum Physics, S. Gasiorowicz, John Wiley & Sons, 1996.
6) Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles, R.Eisberg and R. Resnick, John Wiley & Sons, 1985.

Planned Learning Activities and Teaching Methods

1. Lecture Method
2. Question-Answer Technique
3. Discussion Method
4. Problem Solving
5. Homework

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 * 0.30 +ASG * 0.10 +FIN * 0.60
5 RST RESIT
6 FCG FINAL COURSE GRADE MTE * 0.30 + ASG * 0.10 + RST * 0.60


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

Further Notes About Assessment Methods

None

Assessment Criteria

1) Students' midterm exams form their success during the semester.
2) Final exam is added to the semester success to form the final semester grade mark.

Language of Instruction

English

Course Policies and Rules

1. Attendance to 70% of course lessons is required.
2. Any attempt of copy will be accompanied with disciplinary investigation.
3. The instructor reserves the right to make practical exams. The grades of these exams will be added to the midterm and final exam grades.

Contact Details for the Lecturer(s)

aylin.yildiz@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 12 4 48
Tutorials 12 2 24
Preparations before/after weekly lectures 12 7 84
Preparing assignments 1 3 3
Preparation for midterm exam 1 5 5
Preparation for final exam 1 5 5
Midterm 1 3 3
Final 1 3 3
TOTAL WORKLOAD (hours) 175

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.1554112121151
LO.2554112121151
LO.3554112121151
LO.4554112121151
LO.5554112121151
LO.6554112121151
LO.7554112121151
LO.8554112121151

CONTACT INFORMATION
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