Physical Sciences: Unified Principles and Fast Estimates
Scope
The Physical Sciences paper stitches together classical mechanics, electromagnetism, quantum mechanics, thermodynamics and statistical mechanics, relativity, solid-state physics, nuclear and particle physics, electronics and mathematical physics. Breadth matters, but short, well-chosen estimates win marks.
In mechanics, expect Lagrangians and Hamiltonians, central-force motion and effective potential, small oscillations, rigid-body moments of inertia, and the distinction between inertial and non-inertial frames.
In electromagnetism, Gauss's law (usable only with symmetry), boundary conditions on fields, the Maxwell equations, Poynting vector, and gauge choice.
In quantum mechanics, operators and commutators, the uncertainty principle, angular momentum algebra, the hydrogen spectrum including degeneracy, identical particles with symmetric or antisymmetric wavefunctions, and perturbation theory.
In thermodynamics and statistical mechanics, distinguish canonical from grand canonical ensembles, Fermi–Dirac from Bose–Einstein statistics, and classical from quantum regimes (thermal wavelength versus interparticle spacing).
Traps
Sign errors in work and in the first law; computing Gauss's law without the required symmetry; forgetting degeneracy factors in partition functions; assuming all hydrogen levels of a given shell are split without a perturbation that does that; mixing up eigenvalues with expectation values; and ignoring relativistic corrections where v is not small.
Worked example
Use hc ≈ 1240 eV·nm: a 620 nm photon carries about 2 eV, and visible photons lie in the 1.8–3.1 eV range. This single constant converts wavelength questions into instant energy estimates and flags whether a process is optically accessible. Similarly, [x, p] = iħ immediately fixes commutators and uncertainty products.