Quantum Physics

— A Notebook —

from Planck (1900) to Entanglement

Lab notebook of K. Ning · vol. III

May 2026

1900 · Planck

Energy comes in lumps.

Studying blackbody radiation, Max Planck made a desperate ad-hoc fix: assume oscillators can only emit/absorb energy in discrete chunks — quanta .

E = h·ν

h = 6.626 × 10⁻³⁴ J·s tiny!
Planck himself thought it was just a math trick.
It wasn't. The classical world cracked open.

"An act of desperation," he later called it.

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1905 · Einstein

The photoelectric effect — light is granular too.

Shine light on metal → electrons pop out. Classical theory predicted: brighter light = more energetic electrons.

Wrong. What matters is frequency, not intensity. Below a threshold ν₀, nothing happens — no matter how bright.

KE = hν − φ

Light arrives in discrete packets — photons .
Won Einstein the 1921 Nobel (not relativity!).
Wave-particle duality is now real.

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1913 · Bohr

Electrons live on discrete orbits.

Hydrogen's spectrum had specific colors — not a smear. Bohr postulated electrons orbit only at quantized angular momentum:

L = n·ℏ (n = 1, 2, 3, ...)

Photons emitted when electrons jump down.
Explained the Rydberg formula.
Crude model — but a huge step.

Sketch: Bohr atom (hydrogen)

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1924 · de Broglie

Matter has wave nature.

Louis de Broglie (in his PhD thesis!): if light waves act like particles, why shouldn't particles act like waves?

λ = h / p

Every electron is also a wave

Confirmed by Davisson–Germer (1927): electrons diffract through crystals.
Even buckyballs (C₆₀) show interference. Even molecules of 2000+ atoms.

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1926–27 · Schrödinger & Heisenberg

The wavefunction. The uncertainty principle.

Schrödinger wrote the equation that governs the wavefunction Ψ:

iℏ ∂Ψ/∂t = Ĥ Ψ

Almost simultaneously, Heisenberg showed you cannot pin down both position and momentum:

Δx · Δp ≥ ℏ/2

Not a measurement clumsiness — it's fundamental.
|Ψ|² gives the probability of finding the particle (Born rule).
The same physics, two formalisms — wave mechanics & matrix mechanics.

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The Double-Slit Experiment

"All of quantum mechanics in one experiment." — Feynman

Send one electron at a time → fringes still build up.

Each particle goes through both slits as a wave — but lands as a single point. Try to peek at which slit, and the fringes vanish.

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1935 · EPR

"Spooky action at a distance."

Einstein, Podolsky & Rosen wrote a paper attacking QM as incomplete. Their target: entanglement.

Pair two particles so their spins are correlated. Send them light-years apart. Measure one — instantly the other's outcome is fixed. How? They must have carried the answer all along, said EPR. Reality must be locally pre-determined by hidden variables.

Schrödinger coined "Verschränkung" — entanglement — that year.
Einstein: "God does not play dice."
Bohr: it's fine, you just can't talk about properties before measurement.

For 30 years the debate seemed philosophical. Then Bell took up the pen.

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1964 · Bell's Theorem

Hidden variables — ruled out.

John Bell derived an inequality that any local-hidden-variable theory must obey:

|S| ≤ 2 (local realism)

Quantum mechanics predicts |S| = 2√2 ≈ 2.83.

Aspect (1982), Zeilinger, Clauser — experiment after experiment violates Bell.
2015: loophole-free tests in Delft, Vienna, NIST.
2022 Nobel Prize.
Conclusion: no local hidden variables. Reality is non-local or non-real.

Pick your poison.

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Decoherence & Measurement

Why doesn't my coffee cup superpose?

Quantum systems don't sit in a vacuum — they entangle with their environment (photons, air molecules, phonons) at femtosecond speed.

This decoherence rapidly washes out interference for macroscopic objects. The cat is dead OR alive, in our local "branch."

Decoherence ≠ collapse. It explains the appearance of classicality.
Why we never see Schrödinger's cat suspended in superposition.
Why quantum computers need millikelvin shielding.

Schrödinger's cat — a thought experiment, not a how-to

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Quantum, in Your Pocket

Modern applications.

Lasers — stimulated emission (Einstein, 1917). From DVD players to LIDAR.
Semiconductors — band theory is quantum mechanics. Every transistor in your phone.
MRI — nuclear-spin precession, a direct quantum effect.
GPS — atomic clocks tuned to a Cs hyperfine transition.
Solar cells, LEDs — photoelectric effect & bandgaps.
Quantum computers — superposition + entanglement as compute resources. Shor's algorithm, error-corrected qubits, NISQ era → fault tolerance.

~30% of US GDP touches quantum tech.

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What IS the Wavefunction?

The unresolved question.

The math works. But what is Ψ made of?

Copenhagen (Bohr, Heisenberg) — Ψ is a tool for predicting measurements. Don't ask more. "Shut up and calculate."
Many-Worlds (Everett, 1957) — Ψ never collapses; the universe branches. Every outcome happens, somewhere.
QBism (Fuchs, Caves) — Ψ is an agent's belief, a subjective Bayesian wager.
Pilot-wave (de Broglie–Bohm) — particles do have positions, guided by a non-local wave.
Objective collapse (GRW, Penrose) — collapse is real and physical.

All make the same predictions today. The pen, here, hesitates. pick one ☺

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