FY507: Introductory quantum mechanics (10 ECTS)

STADS: 07011101

Level
Bachelor course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: mlomholt@sdu.dk

Additional teachers
Ilia@sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
1. del samlæses med FY521. 2. del samlæses med FY522.

Prerequisites:
None

Academic preconditions:
Knowledge of FF502 Physics and Mathematics as well as FF505 Computational Science or KE529 Mathematic methods in Chemistry and Nanoscience is expected.

Course introduction
First part of the semester: 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.

Second part of the semester: To achieve an operational knowledge of quantum mechanics of simple systems.

Expected learning outcome
After completing the course the student is expected to be able to:
First part of the semester:

1. qualitatively explain how the wave function of a stationary state depends on the energy of the particle and the form of the potential
2. solve the Schrödinger equation for simple one-dimensional cases, both analytically and numerically
3. explain the energy spectrum of the infinite well, the harmonic oscillator, and the Hydrogen atom and know the form of the associated wave functions
4. calculate particle reflection and transmission probabilities for scattering in one dimension
5. understand how band structure emerges in one-dimensional periodic potentials.

Second part of the semester:

1. apply different analytical methods to characterize simple quantum systems
2. use different abstract formulations of quantum mechanics
3. work with angular momentum
4. perform perturbation calculations
5. use variational methods for approximate calculations

Subject overview
First part of the semester:

1. Schrödinger equation
2. Wave function and its probability interpretation
3. Characterising the wave functions of the stationary states and the energy
4. Specific 1D systems (potentials)
• infinite square well
• finite square well
• harmonic oscillator
• free particle
5. Superposition principle
6. Spherically symmetric systems
7. The Hydrogen atom
8. Periodic potentials
9. Scattering in 1D
10. Tunnel Effect

Second part of the semester:

1. Analytic solutions of the harmonic oscillator using ladder operators
2. The formalism of quantum mechanics
3. The theory of angular momentum
4. Time-independent perturbation theory
5. Time-dependent perturbation theory
6. Variational calculations
7. Uncertainty principle

Literature

• David J. Griffiths: Introduction to Quantum Mechanics, 2nd edition, Pearson Education International.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
First part of the semester: None.

Second part of the semester:

1. Mandatory assignments
2. Presentation of an exercise during the tutorials.

Both a) and b) must be passed. Pass/fail, internal evaluation by teacher.

Assessment and marking:
First part of the semester:

1. An oral exam with internal marking. Marks according to the Danish 7-point marking scale. The examination is based on assignments that have been handed in during the course. (5 ECTS). (07011102).

Second part of the semester:

1. A 4,5 hours written exam. External censorship. Marks according to the Danish 7-point marking scale.  (5 ECTS). (07011112).

A closer description of the exam rules will be posted under 'Course Information' on Blackboard.

Reexamination in the same exam period or immediately thereafter. The mode of exam at the re-examination may differ from the mode of exam at the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 28 hours
Skills training phase: 56 hours, hereof:
 - Tutorials: 42 hours
 - Laboratory exercises: 14 hours

Educational activities

Language
This course is taught in Danish or English, depending on the lecturer.

Remarks
The first part of the course is based on assignment solving that is an integrated part of the teaching. Lectures are given when needed. Computer exercises are used as an “experimental” tool for investigating quantum systems. The course focuses on the understanding of the basic principles, interpretation of quantum behaviour and its use to practical problems

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.