Physics Notes, Solutions, and Related Stuff

I’ve typed up solutions to a few physics problems often set in BSc. courses, some because they aren’t easily found on the web and I’d like to make the lives of fellow labourers that little bit easier, others are here because by writing them up I was drilling them into my head.

I’ve tried to make them as clear as possible in my write-ups from my often less-than-legible notes, but if you have any problems/comments or spot any errors, do get in contact. I hope they’re of some benefit to you.

Particle Physics

• Essay: On the Discovery of Symmetry Violations and Their Effect on the Trajectory of Elementary Particle Physics Research. Forgive the punny title, this is an essay I wrote on symmetry violations in particle physics. Especially if you’re relatively new to particle physics, I’d say this is a good primer of its historical background and major developments, from the foundation of quantum mechanics right up to the Higgs and beyond.
• Fixed Target vs Collider Experiments. Calculation and brief discussion of the difference in energy requirement between a proton-hydrogen fixed target and a beam-colliding pp accelerator like the LHC.
• Mandelstam Variables with Identical Particles, and how the general equations reduce to this case, \(A + A → A + A\).
• Interactions of Charged Particles with Matter. The energy loss of various charged particles passing through a block of iron.

Statistical Physics

GENERAL/FOUNDATIONAL PROBLEMS

• Deriving Stirling’s Formula using an analogy to the Gaussian distribution.
• Particle in a One Dimensional Box. We calculate the classical phase space volume and quantum number of states, and prove adiabatic invariance when the box is enlarged.
• Random Walk of Two Drunks. As light-hearted as maths gets, but a good introduction to random walks.

MICROCANONICAL ENSEMBLE

• System of N Harmonic Oscillators. An important example in statistical physics including the number of accessible states, entropy, and energy of the system.
• Mixture of Two Ideal Gases. Another important example in statistical physics.
• Two-Dimensional Polymer Bundle. A look at a basic model of a two-dimensional polymer from the viewpoint of the microcanonical ensemble. An interesting example not often used in textbooks.

CANONICAL ENSEMBLE

• Modelling a Diatomic Molecule (CO) as a Rigid Rotor.

GRANDCANONICAL ENSEMBLE

• Exchange of Particles between Subsystems.
• Adsorption of Molecules onto a Surface.
• The Maxwell Relations.

THERMODYNAMICS

• Diesel Cycle Efficiency. Deriving a useful result for the efficiency of the Diesel cycle in terms of the compression ratios.
• Reverse Carnot Cycle Efficiency.

This is obviously not meant to be exhaustive of questions or notes relevant to a topic (if you’re looking for lecture notes, you could do worse than the website (archived as it got yoinked) of a friend, JPOffline, but to help you understand the topics I’m passionate about. They’re not primarily intended for you to blindly copy—but of course, you are welcome to do so.

If you find any errors or have any comments, again, do let me know!