Organizational details#

• B.Sc. Physics / IPSP core course, Leipzig University
• Position: Head Teaching Assistant

Literature#

• Classical Mechanics — Goldstein, Safko, Poole
• Analytical Mechanics — Nolting
• Introduction to Electrodynamics — David Griffiths
• (Supplementary) Theoretical Minimum: Special Relativity and Classical Field Theory — Leonard Susskind

Tutorials#

Some tutorials have links to videos recorded by students for their own benefit with my consent.

1. Friday, 18 Oct 2019, (5 PM – 7 PM)

   • Functionals and functional differentiation
   • Concept of a time average of a continuous function
   • A quick synopsis of the concept of a measure (for Math III)

2. Tuesday, 22 Oct 2019, (4:45 PM – 6:45 PM)

   • Functional differentiation examples
   • Principle of least action
   • Derivation of Euler-Lagrange equation using functional calculus

3. Tuesday, 29 Oct 2019, (3:15 PM – 4:45 PM)

   • Understanding Lagrangians
   • Two-stick problem
   • Derivation of the Hamiltonian and corresponding equations of motion

4. Tuesday, 5 Nov 2019, (5 PM – 7 PM) Start of Special Theory of Relativity

   • Invariance of Maxwell’s equations with respect to Galilean transformation
   • Inertial frames of reference
   • Introduction to spacetime diagrams

5. Tuesday, 12 Nov 2019, (5 PM – 7 PM)

   • Relativity of simultaneity
   • Derivation of the Lorentz boost factor using spacetime diagrams
   • General Lorentz transformations

6. Tuesday, 19 Nov 2019, (5 PM – 7 PM)

   • Length contraction and time dilation
   • Invariants in Special Relativity
   • Geometry of Euclidean space vs. Minkowski space

7. Friday, 29 Nov 2019, (5 PM – 7 PM) — Part 1, Part 2

   • Derivation of the Minkowski metric using a moving light clock
   • Light cone and causal structure in Special Relativity
   • Introduction to 4-vectors
   • Physical interpretation of proper time and spacetime interval
   • Relativistic addition of velocities

8. Tuesday, 3 Dec 2019, (5 PM – 7 PM) — Part 1, Part 2, Part 3

   • Repeating 4-vectors
   • 4-velocity vectors, deriving the $\gamma$ factor
   • Deriving the relativistic action $S = -m \int_a^b \sqrt{1-\vec{v}^2}\, \mathrm{d}t$
   • 4-momentum tensor, derivation of relativistic energy

9. Thursday, 6 Dec 2019, (5 PM – 7 PM) — Part 1, Part 2

   • Vectors vs co-vectors (dual vectors)
   • Metric tensors $g_{\mu\nu}$ and the Minkowski metric $\eta_{\mu\nu}$

10. Monday, 10 Dec 2019, (5 PM – 7 PM) — Part 1, Part 2 Start of Classical Field Theory

    • Action principle for fields
    • Lagrangian fields, Euler-Lagrange equation for fields
    • Wave equation in a classical field setting
    • Relativistic / 4-vector fields

    (Data missing from 2–3 lectures in between)

11. Friday, 31 Jan 2020, (5 PM – 7 PM) — Part 1, Part 2

    • Defining 4-current: $J^{\mu} = (\rho, J^{i})$
    • Maxwell’s equations in tensor notation: $\partial_\mu F^{\mu\nu} = \mu_0 J^\mu$, $\quad \partial_\lambda F_{\mu\nu} + \partial_\mu F_{\nu\lambda} + \partial_\nu F_{\lambda\mu} = 0$

12. Tuesday, 04 Feb 2020, (5 PM – 7 PM) — Video

    • Finding a relation between $\vec{E}$ and $\vec{B}$ using Maxwell’s equations and wave equations
    • Different polarizations of the electromagnetic wave