Principles of Physics III - Quantum Mechanics - NBCM241

• Title: Principles of Physics III - Quantum Mechanics
• Guaranteed by: Department of Chemical Physics and Optics (32-KCHFO)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2024
• Semester: winter
• E-Credits: 5
• Hours per week, examination: winter s.:2/2, C+Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Guarantor: doc. Mgr. Jiří Klimeš, Ph.D.
• Teacher(s): doc. Mgr. Tomáš Mančal, Ph.D.; doc. Mgr. Vojtěch Patkóš, Ph.D.; Artur Slobodeniuk, Ph.D.

Annotation

The course Basic Principles of Physics III is the third course in the physics series of the program Science. It provides an introduction to advanced classical mechanics and quantum mechanics. The relevance of quantum-mechanical model systems to chemistry and biology will be also discussed.

Last update: Kapsa Vojtěch, RNDr., CSc. (09.02.2022)

Aim of the course

The aim is to consolidate the knowledge of quantum mechanics gained in chemistry courses and develop the mathematical and physical apparatus needed to apply quantum mechanics to simple systems.

Last update: Kapsa Vojtěch, RNDr., CSc. (09.02.2022)

Course completion requirements

The final mark is based on the oral examination (67%) and the results of tests taken during the course (33%). The oral examination takes place during the examination period and students must first obtain the credit for practical exercises. Credit for exercises is based on the solution of take-home problems (34%) and two tests (midterm and final, each 33%).

Last update: Houfek Karel, doc. RNDr., Ph.D. (17.05.2024)

Literature

1. The Feynman Lectures on Physics, Volume III: Quantum Mechanics, online: https://www.feynmanlectures.caltech.edu/III_toc.html
2. A. I. M. Rae, J. Napolitano, Quantum mechanics, sixth edition, CRC Press, 2016
3. L. E. Ballentine, Quantum mechanics: A modern development, World Scientific, 1998
4. J. Zamastil, J. Benda, T. Uhlířová: Quantum mechanics and electrodynamics, Springer, 2017
5. J. Coopersmith: The Lazy Universe : An Introduction to the Principle of Least Action, Oxford, 2017

Last update: Klimeš Jiří, doc. Mgr., Ph.D. (18.04.2023)

Teaching methods

Students will be provided with the study materials and problem sets and it is expected that students will critically review those materials before exercises.

Last update: Kapsa Vojtěch, RNDr., CSc. (05.02.2022)

Requirements to the exam

The requirements for the exam correspond to the course syllabus to the extent that was given in the lectures.

Last update: Houfek Karel, doc. RNDr., Ph.D. (17.05.2024)

Syllabus

1. Review of classical mechanics
2. Defining experiments of quantum mechanics, spin, entanglement
3. de Broglie and Schrödinger equation
4. Simple solvable 1D systems
5. Harmonic oscillator
6. Approximate methods
7. Angular momentum
8. Hydrogen atom
9. Atoms, molecules, and solids

Last update: Kapsa Vojtěch, RNDr., CSc. (29.09.2025)

Learning outcomes

Students will understand the historical motivation that lead to the

development of quantum mechanics and will gain initial understanding

from connection between quantum and optical waves.

Students will learn and practice mathematical apparatus that will enable

them to efficiently use different approaches that are used to solve

Schroedinger's equation, either exactly or approximately.

They will learn how to use operators and vectors in different representations

and how to go from one representation into another.

Students will learn how is the time-independent Schroedinger's equation

solved for systems with one quantum particle.

They will understand how quantum eigenstates and their energies are obtained

for infinite square well potential, quantum harmonic oscillator,

and hydrogen atom.

Students will understand how the Schroedinger's equation is constructed

for systems that are not solvable analytically and will gain

a basic information about different ways that can be used to solve

such systems.

Last update: Klimeš Jiří, doc. Mgr., Ph.D. (28.01.2026)