Quantum Mechanics for Chemists

Studiewijzer 2023/2024

Globale inhoud

The aim of this course is to give an introduction to elementary quantum mechanics. We will restrict ourselves to the quantum mechanics of single-particle systems. Obviously, (quantum) chemistry is typically concerned with the quantum mechanics of (many) interacting electrons, but this subject will not be addressed in this course. Acquiring some working knowledge of the quantum mechanics of single-particle systems is not only fun but also a necessary prerequisite to understand the quantum theory of many-particle systems which is the subject of many courses in the chemistry master.

The prices content of the course will be developed on canvas.

The first part of the course is very short (1 lecture). Here, we will review some of the problems of classical mechanics which historically lead to the development of quantum mechanics.

In the second part (6 lectures) we will approach quantum mechanics in a rather technical way. Quantum mechanics is typically formulated via states in linear vector spaces and operators acting on these states. We will lay out this formalism and also discuss how this relates to the wave function formalism you might have already encountered before. The topics covered are:

1. Linear vector spaces and quantum states
2. Linear operators, measurement,
3. Basis representation of operators, important bases (eigenbases, real space, momentum space, energy space), commutators
4. Momentum and real space representation of quantum states and wave functions
5. Connections to wave function formalism
6. Time evolution of quantum states, Schrödinger equation

In the third and last part of the course (6 lectures) we will apply this formalism to well-known model systems. These include the hydrogen atom, which is the main model for the electronic structure of finite systems, and electrons in periodic potentials, which is the main model for the electronic structure of periodic systems: The topics covered are:

1. The harmonic oscillator
2. Quantum theory of angular momentum
3. The hydrogen atom
4. Composite quantum systems and spin
5. Quantum states for periodic potentials
6. Band structures of solids

Studiemateriaal

Literatuur

• Lecture Notes published on canvas before the course

• Introduction to quantum mechanics: a time dependent perspective by David J. Tannor (especially chapters 1, 6, and 8).

• Molecular Quantum Mechanics by Atkins and Friedman (especially chapters 1-4)

Leerdoelen

• The student can work with the wave mechanics formulation of quantum mechanics
• The student can work with the operator formulation of quantum mechanics
• The student is able to use techniques of linear algebra in quantum mechanics, in particular unitary transformations, and projectors
• The student can demonstrate understanding of the Heisenberg formalism, picture changes, and time-evolution of quantum systems
• The student can apply those techniques to quantum mechanical model systems (harmonic oscillator, hydrogen atom) and evaluate the results
• The student can understand the independent-particle approximation to many-electron systems.
• The student can apply those techniques to fundamental aspects of band theory and value the results

Onderwijsvormen

• Hoorcollege
• Werkcollege
• Zelfstudie

1.2.1 Monday tutorial
There will be two different types of tutorials. In the Monday tutorial, you will work on assignments yourself which are meant to either recapitulate and broaden the content covered during the lectures, or (mainly in the first week) review some mathematical concepts. Here, Sarina (the TA in this course) will be present and the tutorial is meant to be interactive.

1.2.3 Wednesday tutorial

Starting from second week of the course, during the Wednesday tutorial, the solutions of the assignments from the previous week will be discussed. See below for more info on the assignments.

Verdeling leeractiviteiten

Aanwezigheid

Aanwezigheidseisen opleiding (OER-B):

• Van elke student wordt actieve deelname verwacht aan het onderdeel waarvoor hij staat ingeschreven.
• Als een student door overmacht niet aanwezig kan zijn bij een verplicht onderdeel van het onderdeel, dient hij dit zo snel mogelijk schriftelijk te melden bij de betreffende docent. De docent kan, eventueel na overleg met de studieadviseur, besluiten om de student een vervangende opdracht op te leggen.
• Het is niet toegestaan om verplichte onderdelen van een onderdeel te missen als er geen sprake is van overmacht.
• Bij kwalitatief of kwantitatief onvoldoende deelname, kan de examinator de student uitsluiten van verdere deelname aan het onderdeel of een gedeelte daarvan. Voorwaarden voor voldoende deelname worden van te voren vastgelegd in de studiewijzer en/of op Canvas.

Aanvullende eisen voor dit vak:

Attendance is not required, neither during the lecture nor during the tutorials. 

Toetsing

The final mark of the course is based on a written exam and the assignments.

The final mark is determined in the following way:

1. You need to score at least a 5.5 in the written exam. To score a 5.5, you have to get 50 % of the total possible points in the exam
2. Each Thursday you have the possibility to hand in your assignment sheets which will be graded. Your final mark will be composed of your results in the written exam and the points you achieved for the assignment. The result of the exam counts 80 % and the assignments count 20 %

Inzage toetsing

The grades of the assignments will be published on canvas.

Opdrachten

Each Wednesday after the lecture, you will get a sheet with assignments (via canvas) as homework. You will have one week to work on the assignments and you can hand in your solutions which will then be graded. In total, six assignment sheets will be handed out during the course.

You can either hand in your solutions during the lecture on Wednesday, or via canvas before the start of the Wednesday lecture. You should hand in your solutions in hand-written from. Please write you name on each sheet you hand in. Handing in solutions via canvas (as a scan of your hand-written solutions in PDF format) is possible in case of illness or other reasonable reasons which can be discussed with me.

The assignments are relatively challenging and to solve them successfully you will need to review and understand well the contents of the lecture. You should see them as part of your self-study and completing the assignments will help you to deepen your understanding of the topics covered during the course.

Fraude en plagiaat

Dit vak hanteert de algemene 'Fraude- en plagiaatregeling' van de UvA. Hier wordt nauwkeurig op gecontroleerd. Bij verdenking van fraude of plagiaat wordt de examencommissie van de opleiding ingeschakeld. Zie de Fraude- en plagiaatregeling van de UvA: http://student.uva.nl

Weekplanning

Contactinformatie

Coördinator

• Arno Foerster

Arno Förster: a.t.l.foerster@vu.nl

Docenten

Sarina Sutter (TA):  s.m.sutter@vu.nl