What does this Modern Physics cheat sheet cover?

It has 9 sections: Relativity basics, Relativistic energy, Photoelectric, Compton & matter, Bohr atom, Schrödinger equation, Particle in a box, Uncertainty and Nuclear decay. Together they cover the topics a typical Modern Physics exam tests, including special relativity: time dilation, length contraction, relativistic energy and momentum, photoelectric effect and Compton scattering.

Is the quantum physics cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Modern Physics cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 1 statement before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Modern Physics sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Physics & EngineeringModern Physics

Quantum Physics Cheat Sheet — 1-page PDF

Special relativity, quantum phenomena, atomic models, waves, and nuclear decay. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

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For a specific exam: Modern Physics Final exam study sheet.

1 pageUS Letter
9 sections10 topics
Free previewfull sheet with Unlimited

Preview of the one-page Modern Physics cheat sheet: Special relativity, quantum phenomena, atomic models, waves, and nuclear decay — the whole course, one page

On the sheet

What’s on it

The topics a typical Modern Physics exam tests, all on the one page.

Special relativity: time dilation, length contraction
Relativistic energy and momentum
Photoelectric effect
Compton scattering
De Broglie wavelength
Bohr model
Schrödinger equation
Particle in a box
Uncertainty principle
Nuclear decay and half-life

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The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Relativity basics

Postulates: $c$ same in all inertial frames; laws of physics same in all inertial frames.

Lorentz factor

γ = \frac{1}{1 - v ^{2} / c ^{2}}

$v$ = relative speed, $0 \leq v < c$

Time dilation

Δ t = γ Δ t_{0}

$Δ t_{0}$ proper time; moving clocks run slow

Length contraction

L = L_{0} / γ

$L_{0}$ proper length, parallel to motion

Simultaneity

Δ t^{'} = γ (Δ t - \frac{v Δ x}{c ^{2}})

Lorentz transform for time interval

Time dilationA muon has $Δ t_{0} = 2.2 μ s$ in its rest frame and moves with $v = 0.98 c$ . Find lab lifetime.

$γ = 1/ 1 - 0.9 8^{2} \approx 5.03$ . So $Δ t \approx 11.1 μ s$ .

Watch out:Use $Δ t_{0}$ only for proper time: measured in frame where the two events occur at the same place. Use $L_{0}$ only for proper length: object at rest in that frame.

02Relativistic energy

Momentum

p = γ m v

valid for massive particle

Energy

E = γ m c^{2}

total relativistic energy

03Photoelectric

Stopping potentialIf $h f - ϕ = 2.0 eV$ , find $V_{s}$ .

$e V_{s} = 2.0 eV \Rightarrow V_{s} = 2.0 V$ .

Watch out:Threshold is set by $f$ or $λ$ , not intensity. Bright light below threshold still gives no emission.

04Compton & matter

Compton shift

Δ λ = λ^{'} - λ = \frac{h}{m _{e} c} (1 - cos θ)

$θ$ = photon scattering angle

Compton wavelength

λ_{C} = \frac{h}{m _{e} c}

electron Compton wavelength

de Broglie

λ = \frac{h}{p}

matter-wave wavelength

Particle speed

p \approx m v \Rightarrow λ \approx \frac{h}{m v}

nonrelativistic limit

WavelengthElectron momentum doubles. What happens to $λ$ ?

Since $λ = h / p$ , wavelength halves.

Watch out:Compton shift depends only on scattering angle $θ$ and target mass $m_{e}$ , not on incident intensity.

05Particle in a box

Infinite well

V (x) = 0 (0 < x < L), V = \infty outside

1D box

Allowed states

ψ_{n} (x) = \frac{2}{L} sin (\frac{nπ x}{L})

$n = 1, 2, 3, \dots$

Energies

E_{n} = \frac{n ^{2} h ^{2}}{8 m L ^{2}} = \frac{n ^{2} π ^{2} ℏ ^{2}}{2 m L ^{2}}

quantized levels

Nodes

# nodes = n - 1

excluding walls

Ground stateWhat is $E_{1}$ scaling if $L$ doubles?

$E_{1} \propto 1/ L^{2}$ , so it drops by factor $4$ .

Watch out:Infinite well has no $n = 0$ state. $E_{1} \neq = 0$ because confinement gives zero-point energy.

06Uncertainty

Heisenberg

Δ x Δ p \geq \frac{ℏ}{2}

position-momentum uncertainty

Energy-time

Δ E Δ t \geq \frac{ℏ}{2}

lifetime broadening

Speed estimate

Δ p \approx m Δ v \Rightarrow Δ x Δ v ≳ \frac{ℏ}{2 m}

nonrelativistic estimate

Cheat sheet locked

Also on the full Modern Physics sheet

6 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Relativistic energy

Rest energy
Kinetic energy
Energy-momentum
Photon

Photoelectric

Work function
Einstein equation
Threshold
Max KE
Current trend
Photoelectric dependencies

Bohr atom

Bohr model
Quantization
Hydrogen energy levels
Spectral line
Radius

Schrödinger equation

Time-dependent SE
1D Hamiltonian
Wavefunction
Normalization
Time-independent SE
Boundary conditions

Uncertainty

Measurement limit

Nuclear decay

Activity
Decay law
Activity vs time
Half-life
Mean life
Remaining fraction
Common decay types

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FAQ

Questions

About the Modern Physics sheet and making your own.

What does this Modern Physics cheat sheet cover?: It has 9 sections: Relativity basics, Relativistic energy, Photoelectric, Compton & matter, Bohr atom, Schrödinger equation, Particle in a box, Uncertainty and Nuclear decay. Together they cover the topics a typical Modern Physics exam tests, including special relativity: time dilation, length contraction, relativistic energy and momentum, photoelectric effect and Compton scattering.
Is the quantum physics cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Modern Physics cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it corrected 1 statement before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Modern Physics sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

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Your course, your notes, one page.

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Upload your own Modern Physics slides or notes and get a study sheet in your course’s notation. Your first sheet needs no account, and a free account adds one more. See pricing