Module 02 · Quantum physics
Quantum Physics
Energy comes in quanta, light behaves as particles, and particles behave as waves. These four facts drive thermal imaging, photodetectors, X-ray inspection and electron microscopy — each modelled here as an engineering tool.
Physics → industry. Classical Rayleigh–Jeans theory predicts infinite UV emission (the ultraviolet catastrophe). Planck's hypothesis — oscillator energies E = nhf — fixes it and gives the full spectrum, from which follow Wien's law λmaxT = 2.898×10⁻³ m·K and Stefan's law P = εσAT⁴. Thermal cameras for substations, kilns and motors are specified directly from these laws.
Classical vs quantum
Rayleigh–Jeans vs Planck at the same temperature
Why quantisation is invisible in machines
Planck's oscillator applied to a 2 kg spring
Physics → industry. Electrons leave a surface only if hf > φ — regardless of intensity — and with Kmax = hf − φ. Classical wave theory predicted the opposite on every count. The design rule for light curtains, photomultipliers and image sensors: choose the source wavelength below the cut-off λc = hc/φ, then size optical power for the photocurrent.
Physics → industry. A photon scattering off a free electron behaves like a billiard ball: Δλ = (h/mₑc)(1 − cos θ). Backscattered X-rays lose a predictable amount of energy, so single-sided inspection systems set their detector energy window from this equation.
Physics → industry. Every particle has λ = h/p (de Broglie). Davisson and Germer confirmed it with 54 eV electrons diffracting from nickel (d = 0.215 nm, φ = 50°, λ = 0.165 nm). Electron microscopes use this wavelength — thousands of times shorter than light — to resolve nanometre features in semiconductor fabs.
Physics → industry. A localised particle is a wave packet — a superposition of waves with slightly different k. Crests move at the phase speed vp = ω/k; the envelope (and the energy) moves at the group speed vg = dω/dk, which equals the particle speed u. The same group/phase distinction governs pulse transit in optical fibre.
Physics → industry. Δx·Δp ≥ h/4π and ΔE·Δt ≥ h/4π. Confining an electron to a nanometre channel forces a large momentum spread — a root cause of tunnelling leakage in modern transistors. The energy–time form sets the natural linewidth of lasers and atomic clocks.
Dual nature. Interference and diffraction show light is a wave; blackbody radiation, the photoelectric effect and Compton scattering show it is made of photons with E = hf and p = h/λ. Use this calculator for any source — RF transmitter, laser or X-ray tube.