Course syllabus

# Kvantmekanik och matematiska metoder

Quantum Mechanics and Mathematical Methods

## FMFF15, 7,5 credits, G2 (First Cycle)

## General Information

## Aim

## Learning outcomes

## Contents

## Examination details

## Admission

## Reading list

## Contact and other information

Quantum Mechanics and Mathematical Methods

Valid for: 2023/24

Faculty: Faculty of Engineering, LTH

Decided by: PLED F/Pi

Date of Decision: 2023-04-18

Compulsory for: N4-nf

Elective for: E4, N4-hn

Language of instruction: The course will be given in English on demand

The student should after completing the course have a basic knowledge of quantum mechanics and mathematical methods of physics in order to continue studies in specializations towards nanophysics, highspeed- and nanoelectronics and photonics.

Knowledge and understanding

For a passing grade the student must

- be able to describe and apply the basic postulates of quantum mechanics.
- be able to see the usefulness of quantum theory in some applications.
- know the basics of mathematical methods in physics, especially with regard to applications in quantum physics.
- have applied knowledge of some special functions.

Competences and skills

For a passing grade the student must

- be able to solve and analyze quantum mechanical problems in the field of nanoscience.
- be able to carry out calculations in which the mathematical methods of physics are applied to problems from nanophysics.
- be able to apply the mathematical methods of the course for carrying out a computer project and analyze the results.

Quantum mechanics: Formalism of quantum mechanics: The
Schrödinger equation as eigenvalue equation. Hermitian operators
representing physical quantities, eigenvalues and eigenfunctions.
The harmonic oscillator. Calculation Methodology: First order
perturbation theory, variational methods and matrix
diagonalization. Spherical coordinates and angular momentum.
Applications to the hydrogen atom and atomic structure. Spin and
magnetic interactions. Periodic potential. Bloch wave
functions.

Mathematical Methods: Partial differential equations -
classification and boundary conditions. General information on the
eigenfunctions of operators. Bessel functions. Applications to
cylindrical symmetry problems. Legendre polynomials. Spherical
harmonic functions.

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)

Assessment: Written exam, hand-ins, computer project.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Assumed prior knowledge: FAFA10 Quantum Phenomena and Nanotechnology, FMFF20 Mathematical Methods of Nanotechnology.

The number of participants is limited to: No

The course overlaps following course/s: FAF245, FAFF10, FMA021

- Gunnar Ohlén: Kvantvärldens fenomen, chap. 5-8.
- Mathematics compendium.

Course coordinator: Gillis Carlsson, gillis.carlsson@matfys.lth.se

Course homepage: http://www.matfys.lth.se/education/FMFF15