University Physics IV: Relativity and Quantum Physics

Units

1. 1

   Special relativity

   4 lessons

   1. Einstein's postulates and simultaneitySay why the Michelson-Morley null result and Maxwell's c = 1/√(μ₀ε₀) lead to Einstein's two postulates, define events and inertial frames, use a light clock to show that moving clocks tick slower, and show that two events simultaneous in one frame are not simultaneous in another.
   2. Time dilation and length contractionDefine proper time and proper length, use the Lorentz factor γ = 1/√(1 − v²/c²) in Δt = γΔt₀ and L = L₀/γ, and explain from both frames why cosmic-ray muons born high in the atmosphere reach the ground.
   3. The Lorentz transformation and spacetimeConvert event coordinates between frames with the Lorentz transformation, add velocities relativistically, read events, world lines and light cones on a spacetime diagram, use the invariant interval, and resolve the twin paradox.
   4. Relativistic momentum and energyUse p = γmv, E = γmc², KE = (γ − 1)mc² and E² = (pc)² + (mc²)² for fast electrons and protons, handle massless particles with E = pc, and turn rest-energy differences into the energy released in annihilation and nuclear reactions.
2. 2

   Light as photons

   3 lessons

   1. Blackbody radiation and Planck's quantumRead a blackbody spectrum, use Wien's displacement law and the Stefan-Boltzmann law, show why classical physics predicts an ultraviolet catastrophe, and see how Planck's hypothesis E = nhf, with its Planck law, fits the measured spectrum.
   2. The photoelectric effectDescribe the photoelectric experiment and the stopping potential, find the threshold frequency and work function of a metal, use Einstein's equation K_max = hf − φ, and explain the features of the data that a wave picture of light cannot.
   3. X-rays and Compton scatteringExplain X-ray production with its cutoff wavelength λ_min = hc/eV and characteristic lines, use Bragg's law 2d sin θ = mλ for crystals, and use Compton scattering Δλ = (h/mc)(1 − cos θ) as evidence that photons carry momentum h/λ.
3. 3

   Models of the atom

   2 lessons

   1. Rutherford and the nuclear atomCompare Thomson's plum-pudding model with the alpha-scattering results of Geiger and Marsden, find the closest approach of an alpha particle to a nucleus, read the scattering counts N ∝ 1/sin⁴(θ/2), and explain why Rutherford's planetary atom would collapse classically.
   2. The Bohr model and atomic spectraRead emission and absorption line spectra with the Rydberg formula, derive the Bohr radii and energy levels E_n = −13.6 eV/n² of hydrogen from quantised angular momentum, compute the photons emitted or absorbed in transitions, and state where the model fails.
4. 4

   Matter waves

   2 lessons

   1. De Broglie waves and electron diffractionFind the de Broglie wavelength λ = h/p of an electron, a neutron and a baseball, explain how the Davisson-Germer experiment confirmed it, and say what electrons sent through a double slit one at a time show about wave-particle duality and the electron microscope.
   2. The uncertainty principleBuild a wave packet from many wavelengths and see why a narrow packet needs a wide spread of wave numbers, state Δx Δp ≥ ħ/2 and ΔE Δt ≥ ħ/2, and use them to estimate the minimum energy of an electron in an atom and a proton in a nucleus.
5. 5

   The Schrödinger equation

   5 lessons

   1. The wave function and probabilityUse the Born rule |ψ|² dx as a probability, normalize a wave function, compute expectation values ⟨x⟩ and ⟨x²⟩ and the spread Δx, and read the time-independent Schrödinger equation as a statement about how ψ curves where the energy is above or below the potential.
   2. A particle in an infinite wellSolve the Schrödinger equation for a particle between two infinitely hard walls, find ψ_n = √(2/L) sin(nπx/L) and E_n = n²h²/(8mL²), explain the zero-point energy, compute probabilities of finding the particle in a region, and use the box to estimate the absorption wavelength of a conjugated dye molecule.
   3. The finite well and tunnelingFind the bound states of a finite square well, show that the wave function decays into the walls and the energies fall below the infinite-box values, count the bound states, and use T ≈ e^(−2κL) for a particle passing through a barrier it classically cannot cross, with alpha decay and the scanning tunneling microscope as examples.
   4. The quantum harmonic oscillatorSolve the Schrödinger equation for V = ½kx² to get equally spaced levels E_n = (n + ½)ħω, verify the Gaussian ground state, compare the probability densities with a classical oscillator, and use the levels for the vibration of a diatomic molecule.
   5. The hydrogen atom and quantum numbersDescribe the hydrogen atom in three dimensions with the quantum numbers n, l and m_l, add electron spin m_s and the Stern-Gerlach experiment, read radial probability densities for 1s, 2s and 2p, and use the Pauli exclusion principle to build the shells of the periodic table.
6. 6

   Quantum physics of solids

   2 lessons

   1. Energy bands in solidsExplain how the discrete levels of separate atoms spread into energy bands as atoms come together, distinguish filled, partly filled and empty bands, and use the band gap to say why metals conduct, insulators do not and semiconductors conduct a little.
   2. Semiconductors and the p-n junctionDescribe electrons and holes in an intrinsic semiconductor, show how n-type and p-type doping raise the conductivity, explain the depletion region and built-in potential of a p-n junction, use the diode current I = I_s(e^(eV/kT) − 1), and say how LEDs and solar cells work.
7. 7

   Nuclear physics

   3 lessons

   1. Nuclear structure and binding energyDescribe a nucleus by Z, N and A, find its radius from R = R₀A^(1/3), compute its mass defect and binding energy from atomic masses, and read the binding energy per nucleon curve to see why iron is the most tightly bound.
   2. Radioactive decayWrite alpha, beta and gamma decays so that charge and nucleon number balance, derive the decay law N = N₀e^(−λt) with half-life T½ = ln 2/λ and activity A = λN, and use carbon-14 to date an object.
   3. Nuclear reactions, fission and fusionBalance a nuclear reaction and find its Q value from masses, explain with the binding energy curve why uranium-235 fission and hydrogen fusion both release energy, follow a chain reaction in a reactor, and trace the proton-proton chain of the Sun.