FY544: Quantum mechanics I

The Study Board for Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N500042102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N500042101
ECTS value: 5

Date of Approval: 01-09-2022


Duration: 1 semester

Version: Approved - active

Entry requirements

The course cannot be followed by students who have passed FY521.
The course can not be followed by students who have passed the first part of FY507.

Academic preconditions

Knowledge of FT500: Mechanics and Thermodynamics, FT501: Mathematics and FT504: Electromagnetism and Optics is expected.

Course introduction

The aim of the course is to give the students a basic understanding of the quantum mechanical wave mechanics and its application to different physical phenomena supplemented by an introductory training in the mathematical formalism and problem solving. Furthermore, the fundamental probabilistic nature of quantum mechanics is used in the course as an opportunity to reflect on the philosophy of science behind obtaining new knowledge through experimental observation and the generation of hypotheses.

The course builds on the knowledge acquired in the courses FT500: Mechanics and Thermodynamics, FT501: Mathematics and FT504: Electromagnetism and Optics and gives an academic basis for further studies in quantum physics, as well as studies among others the topics particle physics and solid state physics, that are placed later in the education.

In relation to the competence profile of the degree it is the explicit focus of the course to:

  • give skills to apply physical principles and mathematical tools to formulate and solve physical models
  • give knowledge and understanding of quantum mechanics
  • give ability to acquire new knowledge in an effective and autonomous way and apply this knowledge reflectively
  • give understanding of the method of obtaining scientific knowledge through an interplay between theory and experiment founded in the philosophy of science.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  • Qualitatively describe the basic postulates and statements of quantum mechanics.
  • Qualitatively explain how the wave function of a stationary state depends on the energy of the particle and the form of the potential.
  • Apply the theory quantitatively to solve the Schrödinger equation that governs simple one-dimensional cases, both analytically and numerically.
  • Apply fundamental quantum mechanics principles to determine the energy spectrum and wave functions corresponding to potential wells, the harmonic oscillator, and the Hydrogen atom.
  • Calculate particle reflection and transmission; understand how band structure emerges in one-dimensional periodic potentials.

Content

  1. Hypotheses of quantum mechanics: Physical observables, operators, and expectation values; the Schrödinger equation, the wave function and its statistical interpretation
  2. The uncertainty principle
  3. Vector formalism and matrix formulation of quantum mechanics (“wavefunctions as vectors”), Dirac notation
  4. Bound states in 1D systems: the infinite square well and harmonic oscillator
  5. Scattering states in 1D systems: the free particle and finite square well; reflection and transmission coefficients, quantum tunnelling
  6. Introduction to crystals: Electrons in periodic potentials
  7. Quantum mechanics in three dimensions: orbital angular momentum and the hydrogen atom

Literature

D. J. Griffiths: Introduction to Quantum Mechanics, 3rd edition, Cambridge.
See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

January/June

Tests

Portfolio with oral examination

EKA

N500042102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Duration

Oral examination - 30 minutes

Examination aids

To be announced during the course

ECTS value

5

Additional information

The evaluation is based on project reports.
Oral exam based on the project reports and relevant theoretical subjects from the whole syllabus.
The project reports count for 25% and the oral exam counts for 75% of the overall assessment.

Indicative number of lessons

48 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model i.e. intro, training and study phase.

  • Intro phase (lectures): 32 hours
  • Training phase (tutorials): 16 hours

The intro phase consists of lectures in which the central topics of the course are reviewed. This is done both with general theory and via examples. Even though most of the teaching is based on lectures, there is a strong focus on involving the students via questions and discussions.

In the tutorials, it is expected that the students develop their skills via problem solving and discussions with the teacher and among themselves. The students will solve problems at the blackboard based on initial preparation at home and with the help of everybody else.

Acitivities in the study phase:

  • Study of the lecture notes, textbook and supplemental material.
  • Completion of both analytical and numerical assignments from the classes.

Teacher responsible

Name E-mail Department
Joel Cox cox@mci.sdu.dk Center for Polariton-driven Light-Matter Interactions (POLIMA)
Manuel Meyer mey@sdu.dk Fysik

Timetable

Administrative Unit

Fysik, kemi og Farmaci

Team at Educational Law & Registration

NAT

Offered in

Odense

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Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.