# FY544: Quantum mechanics I

## Entry requirements

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

- 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

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

## Literature

See itslearning for syllabus lists and additional literature references.

## Examination regulations

## Exam element a)

## Timing

## Tests

## Portfolio with oral examination

## EKA

## Assessment

## Grading

## Identification

## Language

## Duration

## Examination aids

## ECTS value

## Additional information

## Indicative number of lessons

## 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.

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

## Teacher responsible

Name | Department | |
---|---|---|

Joel Cox | cox@mci.sdu.dk | Center for Polariton-driven Light-Matter Interactions (POLIMA) |

Manuel Meyer | mey@sdu.dk | Fysik |