MH2426 Quantum Engineering Computations for Nanosystems 7.5 credits

Kvantmekaniska datorberäkningar för nanosystem

Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

Course information

Content and learning outcomes

Course contents *

Repetition of basic quantum mechanics and solid state physics (operators, Schrödinger equation, expectation values, atomic orbitals, solving the Schrödinger equation in spherical coordinates, variational calculus, Bloch’s theorem, Bravais lattice, reciprocal space, band structure, k-points). Electron-electron interaction. Exchange. Correlation. Single-particle model. Effective potential. Homogenous electron gas. Thomas-Fermi model. Functional derivative. Theoretical foundations of DFT. Kohn-Sham equation. DFT model for the helium atom, and solving this model numerically (in Matlab) using finite differences. Calculation and analysis of simpler materials properties using a DFT program package. Assessment of the quality of the calculations. The concepts self-consistency and convergence in DFT calculations. Limitations of DFT calculations. State-of-the-art applications of DFT calculations.

Intended learning outcomes *

When you have finished this course, you will be able to perform DFT calculations of certain simpler materials properties (e.g., density, bulk modulus, band gaps). You will also be able to analyze the results of your calculations, and understand the limitations of DFT calculations. In order to do that, you will have to integrate your computer skills (Matlab, Linux) with your knowledge of quantum mechanics, atomic physics, numerical methods and solid state physics. You will also know about several state-of-the-art applications of DFT calculations.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

IF1621 Kvantmekanik I, or similar like:

  • Quantum mechanics or quantum physics, introductory level.
  • Solid state physics or semiconductor physics, introductory level
  • Numerical methods, introductory level

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

Jos Thijssen, “Computational Physics”, Cambridge University Press, 2007.

Richard M. Martin “Electronic Structure, Basic Theory and Practical Methods”, Cambridge University Press, 2004.

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • HEM1 - Home Assignments, 2.0 credits, Grading scale: P, F
  • NÄR1 - Attendance, 1.5 credits, Grading scale: P, F
  • TEN1 - Examination, 4.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade *

Passed all the home assignments and computer exercises. Attendance at the guest lectures. Written exam at the end of the course.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Anna Delin

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web MH2426

Offered by

ITM/Materials Science and Engineering

Main field of study *

Materials Science and Engineering

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Lars Bergqvist, lbergqv@kth.se, Professor Anna Delin, annadel@kth.se

Ethical approach *

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Supplementary information

Replaces the course MH2425