NWI-WB082
Introduction to Mathematical Physics
Course infoSchedule
Course moduleNWI-WB082
Credits (ECTS)6
CategoryBA (Bachelor)
Language of instructionDutch
Offered byRadboud University; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde;
Lecturer(s)
Coordinator
prof. dr. N.P. Landsman
Other course modules lecturer
Lecturer
prof. dr. N.P. Landsman
Other course modules lecturer
Contactperson for the course
prof. dr. N.P. Landsman
Other course modules lecturer
Academic year2017
Period
KW3-KW4  (05/02/2018 to 02/09/2018)
Starting block
KW3
Course mode
full-time
Remarks-
Registration using OSIRISYes
Course open to students from other facultiesYes
Pre-registrationNo
Waiting listNo
Placement procedure-
Aims
  • Students are to be familiar with the goals and basic mathematical techniques of modern mathematical physics and, are to be prepared for advanced courses and, eventually, doing research in this area.
  • Students are to understand the modern mathematical formulation of classical mechanics via Poisson geometry, as well as the modern mathematical formulation of quantum mechanic via Hilbert spaces. They understand the probabilistic framework of quantum mechanics, 
  • Students are to understand the theory of symmetry in classical mechanics as well as in quantum mechanics, the former via the notion of a momentum map, the latter via Wigner's Theorems.
  • Students understand the phenomenon of spin via the representation theory of SU(2) and SO(3)
  • Students are familiar with the basis theory of unbounded self-adjoint operators, including Stone's Theorem
  • Students know the mathematically correct description of a few model Hamiltonians of quantum mechanics, such as the Hamiltonian of a free particle, the harmonic oscillator Hamiltonian, etc. 
Content

This course is intended for students interested in the connection between mathematics and physics, and is ideal for those taking the double bachelor degree program in math and physics. It prepares, for example, for the new master course on Advanced Mathematical Physics. Following a historical introduction to mathematical physics and its goals, we discuss the modern mathematical formulation of classical mechanics as well as of quantum mechanics, paying special attention for the relationship between these theories.

Literature

• Brian C. Hall, Quantum Theory for Mathematicians (Springer, 2013).
• Lecture Notes by the lecturer

Teaching formats

• 32 hours lecture
• 32 hours problem session
• 104 hours individual study period
Extra information teaching methods:

• 14 x 2 x 45 min lectures
• 14 x 2 x 45 min exercise class

Topics
• Modern mathematical formulation of classical mechanics via Poisson geometry
• Modern mathematical formulation of quantum mechanic via Hilbert spaces
• Symmetry, Momentum Map, Wigner's Theorem
• Spin via the representation theory of SU(2) and SO(3)
• Unitary time-evolution via Stone's Theorem
• Model Hamiltonians of quantum mechanics, such as the Hamiltonian of a free particle, the harmonic oscillator Hamiltonian, etc.

Test information
Written Exam

Prerequisites
Analysis 1, 2, Topology, Introductory Functional Analysis (recommended), basic knowledge of classical mechanics and quantum theory, basic probability theory.

Required materials
Reader
Lecture Notes by the lecturer

Recommended materials
Book
Brian C. Hall, Quantum Theory for Mathematicians (Springer, 2013).

Instructional modes
Course

General
• 14 x 2 x 45 min lectures • 14 x 2 x 45 min exercise class

Lecture

Tutorial

Zelfstudie

Tests
Tentamen
Test weight1
OpportunitiesBlock KW4, Block KW4