# FYS2140 - Quantum physics

## Course description

## Schedule, syllabus and examination date

**Choose semester**

## Course content

Blackbody radiation, photoelectric effect, X-rays, Compton scattering, the Bohr atom, matter waves, Heisenbergs uncertainty relation, the Schrödinger equation and wave function, simple quantum mechanical systems in one dimension, tunneling, the formalism of quantum mechanics, quantum mechanics in three dimensions, Hydrogen atom, spin, Paulis exclusion principle, the periodic system, atoms and molecules, some basic nuclear-, particle and condensed matter physics

## Learning outcome

Learning outcomes

Students are expected to reach the following learning goals:

1) Knowledge

- Know the background for and the main features in the historical development of quantum mechanics.

- Explain, qualitatively and quantitatively, the role of photons in understanding phenonema such as the photoelectric effect, X-rays and Compton scattering.

- Gain an understanding of the historical importance of Bohr's model of the hydrogen atom, its strenghts and weaknesses, and how it differs from the Schrödinger equation description of the hydrogen atom.

- Be able to discuss and interpret experiments displaying wavelike behaviour of matter, and how this motivates the need to replace classical mechanics by a wave equation of motion for matter (the Schrödinger equation).

- Understand the central concepts and principles of quantum mechanics: the Schrödinger equation, the wave function and its physical interpretation, stationary and non-stationary states, time evolution and expectation values.

- Interpret and discuss physical phenonema in light of the uncertainty relation.

- Gain a basic understanding of the formalism and 'language' of quantum mechanics and how it relates to linear algebra.

- Grasp the concepts of spin and angular momentum, as well as their quantization- and addition rules. Explain the Zeeman affect and spin orbit coupling.

- Be able to define the concepts of identical particles and quantum statistics, and understand the role played by quantum statistics in e.g. the structure of the periodic table.

- Explain physical properties of elementary particles, nucleons, atoms, molecules and solids (band structure) based on quantum mechanics.

2) Skills

The students are expected to master the basic mathematical skills that will be required throughout the course, such as the use of complex numbers and complex valued functions, simple differential equations, Gaussian integrals and basic linear algebra. (Some of the most important math will be refreshed in the first assignment of the course.)

- Be able to use computer tools to solve simple numerical problems.

- Be able to independently solve the Schrödinger equation for simple one-dimensional systems -- the ones explicitly taught (e.g. square well, harmonic oscillator, potential barrier), as well as similar, new ones.

- Use the solution to compute probabilities, expectation values, uncertainties and time evolution.

- Give concise physical interpretations, and arguments for the validity of the mathematical solutions.

- Similarly, solve simple problems in two and three dimensions in various coordinate systems, e.g. by using separation of variables in the Schrödinger equation.

- Perform calculations on systems of identical particles, e.g. determine the symmetry properties of the wave function, and the total spin.

## Admission

Students at UiO must apply for courses in StudentWeb.

**International applicants**, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

## Prerequisites

### Formal prerequisite knowledge

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

One of these:

- Mathematics R1
- Mathematics (S1+S2)

And and in addition one of these:

- Mathematics (R1+R2)
- Physics (1+2)
- Chemistry (1+2)
- Biology (1+2)
- Information technology (1+2)
- Geosciences (1+2)
- Technology and theories of research (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies. Read more about special admission requirements.

### Recommended previous knowledge

MAT1100 - Calculus, MAT1110 - Calculus and linear algebra, MAT1120 - Linear algebra, FYS-MEK1110 - Mechanics and FYS1120 - Electromagnetism

We also recommend that students take FYS2130 - Waves and oscillations concurrently with this course to profit maximally from it.

## Overlapping courses

10 credits overlap against FY102, which was offered the last time in spring semester 2003.

## Teaching

4 lectures a 45 min. each per week, 3 hours of kolloquium and 4 hours problemsolving. The course will include 12 sets of compulsory exercises. Minimum six out of twelve compulsory exercises (min. two of the exercises 1-4, two of the exercises 5-8 and two of the exercises 9-12) have to be handed in and approved during the semester. These exercises include analytic, numerical and experimental topics. In addition there will be a home exam.

## Examination

A written home assignment with approx. 20 % weight (medio March). Final written exam (4 hours) with approx. 80 % weight (primo June). The students have to pass in both elements in order to pass the course. In addition a minimum of six compulsory exercises have to be passed in order to sit for the final exam.

### Examination support material

Allowed aids: Rottman: "Matematisk formelsamling." Øgrim and Lian: "Fysiske størrelser og enheter" or Angell and Lian: "Fysiske størrelser og enheter". Approved calculator. One A4 sheets of paper with notes (both sides).

### Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

### Explanations and appeals

### Resit an examination

Re-scheduled exams are offered at the beginning of the next semester for students who:

- can document a valid reason for absence from the regular exam (e.g. illness before or during the exam)
- withdraw during the exam
- do not successfully complete the exam during the previous term.

Read more about re-scheduled exams.

### Special examination arrangements

If you have a disability or a health problem that entails significant inconvenience in an examination situation, you may be considered for special examination arrangements. Mothers who are breastfeeding may apply for extra time to complete the exam.

## Evaluation

Feedback from our students is essential to us in our efforts to ensure and further improve the high quality of our programmes and courses. All courses are subject to continuous evaluation. At regular intervals we also ask students on a particular course to participate in a more comprehensive, periodic evaluation of this course.