Quantum physics (for AP Physics 2)

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Wave-particle duality (for punctuated isolation scenarios)

wavefunction – represents vibration across space particle – concept of point-like object used for book-

keeping of possible future point-like interactions

∆Prob |𝜓 𝑥 | ∆𝑥

Light

Wave characteristics

𝑐 𝜆𝑓

𝑐 3.00 10ms

Particle characteristics

𝐸 ℎ𝑓

𝑝𝐸

𝑐ℎ𝜆

ℎ 6.626 10 J ⋅ s

Photoelectric effect

ℎ𝑓 𝜙 𝐾

Quantum physics (for AP Physics 2)

Page 2 of 3 DAVID LIAO.COM

Wave-particle duality (for punctuated isolation scenarios)

wavefunction – represents vibration across space particle – concept of point-like object used for book-

keeping of possible future point-like interactions

∆Prob |𝜓 𝑥 | ∆𝑥

Matter

Particle characteristics

Wave characteristics

de Broglie hypothesis

Guess: Relationships between wave and mechanical features for light hold for matter.

𝜆ℎ𝑝

𝑓𝐸ℎ

Particle diffraction

Using the de Broglie wavelength leads to correct predictions of diffraction patterns.

Particles that are confined have quantized energies

Standing waves in physical media

Spatial confinement leads to standing waves at discretely separated frequencies.

Standing probability amplitude waves

Spatial confinement leads to standing wavefunctions with discretely separated frequencies, and, thus, discretely separated energies.

Bohr orbits

𝑐 2𝜋𝑟 𝑛𝜆 𝑛 1,2,3, …

𝑅 0.0529 nm𝑛𝑍

𝐸 13.6 eV𝑍𝑛

Quantum physics (for AP Physics 2)

Page 3 of 3 DAVID LIAO.COM

Light and matter exchange energy

The colors of light absorbed and emitted by gas can be computed by conceptualizing light in terms of particles while also conceptualizing electrons in terms of probability amplitude waves.

ℎ𝑓 𝑈 , ℎ𝑓 𝑈 ,

Emission spectra Absorption spectra