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Quantum Mechanics — The Uncertainty Principle
22:30
🎙 1240w
Allan Adams · MIT 8.04
Δx · Δp ≥ ℏ/2the uncertainty principle
22:30 / 38:50
Transcribing "…so the more precisely we know position, the less we can say about momentum…"
✦Quick check
As you measure an electron's position more and more sharply, its momentum becomes:
LIVE22:30· 1240w · 8 frames
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21:50
You · voice
Where does the ℏ/2 bound actually come from?
21:51
AI
It falls out of treating position and momentum as Fourier conjugates: a wave packet narrow in x is necessarily broad in k, and p = ℏk. The ℏ/2 is the tightest the product can get, hit only by a Gaussian packet.
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Your lecture quest
Lecture quest · 0/5 mastered
Topics — your synthesis, in your words
§1Light as quanta: the photoelectric effectUpcoming00:00–07:30
In one line — when you turn light brighter, what do you get more of?
In your words

Opens when you reach this topic.
§2Electrons as waves: de BroglieUpcoming07:30–15:40
Why do we never notice the wavelength of a cricket ball?
In your words

Opens when you reach this topic.
§3The uncertainty principleUpcoming15:40–24:10
In one line, what does this inequality forbid you from knowing at once?
In your words

Opens when you reach this topic.
§4Wave packets and localisationUpcoming24:10–31:20
Δk · Δx ≈ 1⊞ AI placed · as you reach it
To pin the position down tighter, what do you have to give up?
In your words

Opens when you reach this topic.
§5What 'position' means for an electronUpcoming31:20–38:50
In your words — does the electron have a definite position before you measure it?
In your words

Opens when you reach this topic.
Equations (3)
Auto-scanned from the transcript every 15s. Each equation has a Derive button for a step-by-step walkthrough.
[1]Heisenberg uncertainty22:30
Δx · Δp ≥ ℏ/2

Stated as the product of the spreads in position and momentum has a hard floor.

[2]de Broglie wavelength12:05
λ = h/p

Every particle has a wavelength set by its momentum.

[3]Photon energy03:40
E = hf

Light arrives in quanta whose energy scales with frequency.

Cards (6)
Flash card
What does brightness add to a beam of light?
More photons — not more energetic ones. E = hf is fixed by frequency.
Flash card
What is the de Broglie wavelength of a particle?
λ = h/p — inversely proportional to momentum.
Flash card
State the uncertainty principle.
Δx · Δp ≥ ℏ/2 — you cannot sharpen both at once.
Frames (8)
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Δx · Δp ≥ ℏ/2
22:30
λ = h/p
12:05
wave packet
25:40
E = hf
03:40
21:40So the question we keep coming back to is: how well can you simultaneously know where a particle is and how fast it's moving?
22:05And the answer, which is genuinely strange, is that there's a hard limit — Δx times Δp is bounded below by ℏ over 2.
22:30The more precisely we know position, the less we can say about momentum. This isn't a statement about clumsy instruments.
Simulations (2)
Interactive simulations tied to this lecture. Drag the sliders to see how the wavefunction responds.
Simulation
Wave packet — position vs momentum spread
Narrow the packet in x and watch Δp widen. The product Δx·Δp never drops below ℏ/2.
Simulation
Single-slit diffraction
Shrink the slit; the pattern spreads — sharper position buys a wider momentum spread.
Tangents (3)
Short detours and 'why does this matter' asides the lecturer touched on.
Tangent
Why ℏ and not h?
The reduced Planck constant ℏ = h/2π falls out naturally from the Fourier / angular forms.
Tangent
Heisenberg's microscope
A useful heuristic — but the bound is deeper than measurement disturbance.
Tangent
Does this apply to a cricket ball?
Yes — but ℏ is so small the spread is utterly unobservable at that scale.
Problem set
Problems generated from this lecture's objectives, graded with step-by-step feedback.
Problem · 1
An electron is localised to Δx = 1 nm. Estimate the minimum Δp and the corresponding velocity spread.
Problem · 2
Show that a Gaussian wave packet saturates the bound, i.e. Δx·Δp = ℏ/2.
Full notebook
Your whole notebook across lessons — this lecture is filed under Quantum Mechanics.
Notebook
Quantum Mechanics — The Uncertainty Principle
5 objectives · 2 mastered · 3 clips filed · last edited just now
Notebook
Quantum Mechanics — de Broglie & matter waves
4 objectives · 4 mastered · filed last week
Δx · Δp ≥ ℏ/2
Allan Adams · 22:30
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Quantum Mechanics — The Uncertainty Principle · 22 min
6 cards·8 frames·1240 words
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