Quantum Physics 2

Quantumfysica 2

Course manual 2025/2026

Course content

This course is the continuation of the Quantum Physics 1 and Quantum Concepts courses. Starting from the formalism of quantum mechanics, the course then moves to discuss the quantum mechanics of three-dimensional systems and the hydrogen atom, systems of identical particles, and finishes with a discussion of time-independent perturbation theory and the variational principle. The course combines a more theoretical discussion of the principles and results of Quantum Mechanics with a review of important applications in fields from atomic physics and material science to astrophysics and particle physics.

The applications discussed in this course are closely related to follow-up courses in the Physics and Astronomy BSc program:

• Advanced Quantum Physics
• Atomic Physics
• Light-Matter interactions
• Computational Quantum Mechanics (honours)

In this course, we will mostly follow the structure of the textbook "Introduction to Quantum Mechanics" by Griffiths. The course contents are divided into two main parts: Theory and Applications.

Part I: Theory
• Chapters 3.1, 3.2, 3.3, 3.4, 3.5, 3.6: The formalism of quantum mechanics. States and operators in Hilbert space. Eigenfunctions and eigenvalues of Hermitian operators. Expectation values of physical observables. Generalised statistical interpretation and Heisenberg’s uncertainty principle revisited. Vectors and operators in Hilbert space. The Dirac notation in quantum mechanics.
• Chapters 4.1, 4.2, 4.3, 4.4: Quantum mechanics of three-dimensional systems. The Schrödinger equation in three dimensions and angular momentum. The infinite spherical well. The hydrogen atom. Solutions of the radial and angular equations and their properties. Angular momentum in three dimensions. Spin in quantum mechanics. Addition of spin and angular momenta.
• Chapters 5.1, 5.2, 5.3: Identical particles in quantum mechanics. Bosons and fermions. Implications for multi-electron atoms and for the structure of matter. The periodic table. The quantum theory of solids and the free-electron gas. The band structure of solids. 
• Chapters 6.1, 6.2, 6.3, 6.4: Symmetries and conservation laws in quantum mechanics and their implications. Transformations of states and operators. Translational symmetry. Conservation laws. Parity selection rules.

Part II: Applications
• Chapters 7.1, 7.2, 7.3: Time-independent perturbation theory. Applications to non-degenerate and degenerate systems. Perturbation theory and the fine structure of hydrogen atoms. Spin-orbit coupling.
• Chapters 8.1, 8.2, 8.3: The variational principle and the ground state of complex systems. Application to the ground state of helium and the hydrogen molecular ion.

Study materials

Literature

• Griffiths, Introduction to Quantum Mechanics, 3rd edition

Syllabus

• (Canvas)

Other

• Lectures notes (Canvas)

• Exercises + Solutions (Canvas)

Objectives

• Formulate quantum states and observables in Hilbert space (Dirac notation); work with Hermitian operators, commutators, expectation values, and uncertainties.
• Solve the 3D Schrödinger equation for central potentials; use spherical harmonics and angular-momentum algebra.
• Analyze fundamental systems (particle on a ring/sphere, infinite spherical well) and derive the hydrogen spectrum and eigenfunctions, including degeneracies.
• Describe spin and perform addition of angular momenta to build coupled bases and interpret quantum numbers.
• Construct properly (anti)symmetrized many-particle states and explain consequences for multi-electron atoms, the periodic table, and qualitative band/fermion-gas models.
• Use symmetries (translations, rotations, parity) to infer conservation laws and simplify problems.
• Apply time-independent perturbation theory (non-degenerate/degenerate) and the variational principle; compute fine-structure (spin–orbit) corrections in hydrogen and estimate the helium ground state.

Teaching methods

• Lecture
• Seminar
• Self-study

Learning activities

Attendance

Programme's requirements concerning attendance (TER-B):

• Each student is expected to participate actively in each component of the programme that he/she signed up for. A student that does not attend the first two seminars of a course, will be administratively removed from the seminar group. A request for reregistration for the seminars can be applied to the programme coordinator.
• If a student cannot attend an obligatory component of a programme's component due to circumstances beyond his control, he must report in writing to the relevant teacher as soon as possible. The teacher, if necessary after consulting the study adviser, may decide to issue the student a replacing assignment.
• It is not allowed to miss obligatory commponents of the programme if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are set down in advance in the course manual.

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

The course will be taught fully in English. Students are allowed to use Dutch for exercises, minitests, and the exam. This course is not open for double bachelor students Mathematics & Physics.

Contact information

Coordinator

• dr. M. Beyer