A Level Quantum Physics Hub
A Level Quantum Physics hub covering photons, matter waves, wavefunctions, uncertainty, the infinite square well and atomic line spectra.
Learning goals
- Use photon energy and momentum and analyse the photoelectric effect.
- Apply de Broglie wavelength and wave-particle evidence.
- Interpret wavefunctions, probability density and superposition.
- Apply uncertainty and infinite-square-well energy quantisation.
- Analyse atomic energy levels and emission or absorption spectra.
Quantum Physics links experimental evidence to models that are not classical particles or classical waves. Follow the evidence first, then learn how wavefunctions, uncertainty and boundary conditions predict measurable probabilities and discrete energies.
Prerequisites: Waves, Work, Energy and Power, momentum and graph gradients.
Route: photon evidence and momentum → matter waves → wavefunction and superposition → uncertainty → particle in a box → atomic energy levels and spectra.
Scope note: the core route below follows the current 9478 syllabus. Stopping-potential methods, the Bohr model, X-ray production, the Schrödinger equation and tunnelling are retained as clearly labelled support or extension material.
Lessons
Work through these lessons in order.
- Photon evidence, energy and momentum
- Matter-wave evidence and de Broglie wavelength
- Wavefunctions, probability density and superposition
- Uncertainty and the one-dimensional infinite square well
- Atomic energy levels and line spectra
- Photoelectric Effect
Understand the photoelectric effect, including threshold frequency, intensity vs kinetic energy, and stopping potential with exam-ready explanations (A Level Physics).
- Wave Particle Duality
Connect photon and wave models: E = hf, p = E/c = h/λ, and de Broglie wavelength λ = h/p for matter waves (A Level Physics).
- Electron Diffraction & Single-Particle Interference
Explain how electron diffraction and single-particle double-slit interference provide evidence for the wave nature of particles, and use λ = h/p to solve problems (A Level Physics).
- Wavefunction & Probability Density (Normalisation)
Use |ψ|^2 as a probability density and calculate normalisation constants for square and sinusoidal wavefunctions (A Level Physics).
- Heisenberg's Uncertainty Principle (A Level)
Use Heisenberg’s uncertainty principle to link position localisation to momentum spread, and solve ΔxΔp questions with exam-safe wording (A Level Physics).
- Particle In A Box (Infinite Square Well)
Use standing-wave wavefunctions and En = n^2 h^2 / (8mL^2) for a particle in a 1D infinite square well (A Level Physics).
- Energy Level Diagram For Hydrogen
Read a hydrogen energy level diagram, interpret negative energies and ionisation energy, and use ΔE = hf = hc/λ for photon emission/absorption (A Level Physics).
- Line Spectra
Distinguish emission and absorption line spectra, explain why spectra are discrete, and use ΔE = hf = hc/λ for transitions (A Level Physics).
- Observations of Photoelectric Effect · Supporting
Learn the four key experimental observations of the photoelectric effect and what each implies about photons, intensity and frequency (A Level Physics).
- Understanding Photoelectric Effect · Supporting
Use the photon model (E = hf) to explain threshold frequency, immediate emission, and the frequency/intensity trends in the photoelectric effect (A Level Physics).
- Failure of Classical Wave Theory · Supporting
See why classical wave ideas fail to explain key photoelectric effect observations, motivating the photon model (A Level Physics).
- Einstein's Photoelectric Equation · Supporting
Apply Einstein’s photoelectric equation Kmax = hf − Φ and the stopping potential relation Kmax = eVs, including graph interpretation (A Level Physics).
- Bohr Model of The Atom · Supporting
Use the Bohr model as a simple picture for discrete energy levels and photon emission/absorption (ΔE = hf), with clear limitations (A Level Physics).
- The Schrodinger Equation And Wave Function · Supporting
Understand what the wavefunction represents, how probability density works, and how to normalise simple wavefunctions; Schrödinger equation is included as optional context (A Level Physics).
Revision
Evidence map
An observation is not the model itself. In an explanation question, name the observation, state the classical expectation if relevant, then show how the quantum relationship accounts for it.
Quick reference
| Idea | Relationship | Meaning or condition |
|---|---|---|
| Photon energy | E = hf = hc/λ | one photon transfers one quantum of energy |
| Photon momentum | p = E/c = h/λ | photons are massless but carry momentum |
| de Broglie wavelength | λ = h/p | larger particle momentum means shorter wavelength |
| Probability in an interval | P(a ≤ x ≤ b) = ∫ₐ^b|ψ|² dx | probability is area under probability density |
| Normalisation | ∫|ψ|² dx = 1 | the particle must be found somewhere |
| Uncertainty | Δ xΔ p≳ h | greater localisation requires a broader momentum spread |
| Infinite square well | Eₙ = n²h²/(8mL²) | n = 1,2,3,…; n = 0 is not allowed |
| Atomic transition | |Δ E| = hf = hc/λ | photon energy must match an allowed level gap |
Constants: h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.
Wavefunction checkpoint
For a one-dimensional wavefunction, |ψ|² has units of m⁻¹. It is a density; only an integral over a finite interval is a probability.
Atomic transition checkpoint
Use the magnitude of the energy difference for photon calculations. Then use the direction of the transition to decide whether the photon is absorbed or emitted.
Exam traps
- Intensity cannot overcome a threshold-frequency failure. At fixed frequency, intensity changes photon rate, not energy per photon.
- Evidence must be matched to the claim. Photoelectric threshold supports photon behaviour; diffraction and interference support wave behaviour.
- ψ is not probability. Square its magnitude, then integrate over the stated region.
- Uncertainty is not just instrument error. It is intrinsic to a localised quantum state.
- A box has no n = 0 state. Nodes at both walls require at least one half-wavelength inside the box.
- Absorption is selective. A photon is absorbed only when its energy matches an allowed upward energy gap.
Beyond the syllabus
- Further quantum mechanics: Reflection and Transmission, Quantum Tunnelling, and Scanning Tunnelling Microscope.
- Legacy X-ray material: Coolidge X-ray Tube and Features of the X-ray Spectrum.
Practice
Use the quiz to identify a weak outcome, then complete one wavefunction or box question and one energy-level question under timed conditions.
Next hub: Nuclear Physics
Continue with the next resource in this course.
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027