Kvantmekanik och matematiska metoder

Valid for: 2024/25

Faculty: Faculty of Engineering LTH

Decided by: PLED F/Pi

Date of Decision: 2024-04-15

Effective: 2024-05-08

Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified

Mandatory 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 account for and explain the basic postulates of quantum mechanics.
- be able to explain basic theoretical concepts and models within quantum mechanics and explain which mathematical concepts and methods are used to describe them.
- be able to exemplify, analyze and problematize the use of basic quantum mechanical models to describe simpler systems in nanophysics and nanoelectronics.
- be able to describe the most important special mathematical functions with application in basic quantum physics.

Competences and skills

For a passing grade the student must

- be able to formulate and solve simpler quantum mechanical problems relevant to the fields of nanophysics and nanoelectronics and broadly be able to assess the plausibility of the solution.
- be able to apply mathematical methods to selected problems in nanophysics and nanoelectronics.
- be able, using mathematical methods, to carry out a computer project and analyze and present the results in written form.

Judgement and approach

For a passing grade the student must

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.

Modules

Code: 0110. Name: Quantum Mechanics and Mathematical Methods.

Credits: 7.5. Grading scale: TH - (U, 3, 4, 5).

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

The number of participants is limited to: No

Kursen överlappar följande kurser:
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