Physics

Quantum sketch

Photons, matter waves, uncertainty.

Basics

Light as packets too

Photoelectric effect: frequency ν must clear a threshold; intensity alone will not. E=hν. Atoms have discrete levels — spectral lines.

Matter waves

Electrons interfere like waves (de Broglie). Allowed “orbits” fit an integer number of wavelengths. Measurement can disturb the state. Probability density is |ψ|².

Formulas

Photon energy

E = h ν = h c / λ

h is Planck’s constant. Shorter λ packs more energy.

Symbols

  • ν frequency

de Broglie

λ = h / p

Larger momentum p → shorter λ, more classical-looking.

Symbols

  • p momentum

Uncertainty (sketch)

Δx Δp ≳ ℏ / 2

Position and momentum cannot both be arbitrarily sharp.

Symbols

  • h / 2π

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