The quantum simulations on mysimulator.uk are grouped into three areas: quantum mechanics fundamentals (wave functions, uncertainty, measurement), quantum information (entanglement, quantum gates, algorithms), and quantum applications (harmonic oscillator, hydrogen atom, tunnelling). Here is what each of the core quantum simulations shows and how to get the most from it.
Fundamentals
Quantum Harmonic Oscillator
Visualise energy eigenstates ψₙ(x) and probability densities |ψₙ(x)|² for any quantum number n. Use the n slider to step from the Gaussian ground state through increasingly oscillatory higher states, observing how nodes accumulate and the wave function extends beyond the classical turning points. The equal energy spacing ΔE = ℏω is shown on the energy level diagram. At large n, toggle the classical overlay to see the correspondence principle at work: the quantum density begins to cluster near the classical turning points, matching the classical probability distribution.
Double-Slit Experiment
The foundational experiment of quantum wave-particle duality. Send single particles through a double slit and watch the interference pattern build up one detection event at a time. Toggle which-path measurement on and off to see the interference pattern appear and disappear — a direct demonstration of wavefunction collapse and complementarity.
Quantum Tunnelling
A wave packet approaches a rectangular potential barrier. Adjust barrier height and width to control the transmission coefficient. Observe the transmitted and reflected components of the wave function and read off the exact tunnelling probability. This is the physics behind scanning tunnelling microscopes, nuclear alpha decay, and transistor gate oxide.
Quantum Information
Bell Inequality
The most direct demonstration that quantum mechanics is incompatible with local hidden variable theories. The simulation runs CHSH inequality tests on entangled qubit pairs. Sweep the measurement angle and watch the correlation curve exceed the classical bound of 2 — reaching the Tsirelson bound of 2√2 for optimal entangled states. The gap between the classical and quantum curves is what Bell called "the most important discovery in physics."
Bloch Sphere
Any pure qubit state can be represented as a point on the surface of the Bloch sphere. Apply quantum gates (X, Y, Z, H, S, T) and watch the state vector rotate. Compose gate sequences and verify that the Hadamard gate maps the computational basis to the equatorial plane. Essential for anyone studying quantum computing: the Bloch sphere is the geometry of the qubit.
Grover's Search Algorithm
Grover's algorithm finds a marked item in an unsorted database of N entries in O(√N) steps rather than the classical O(N). The simulation visualises the amplitude amplification process: each iteration the amplitude of the target state grows while others shrink. Watch the probability of measuring the correct answer approach 1 after ⌊π√N/4⌋ iterations, then decrease again as the algorithm overshoots. Set N and choose how many iterations to run.
Where to start: If you are new to quantum simulations, begin with the Quantum Harmonic Oscillator (set n = 0, then increase slowly) and the Double-Slit Experiment (run in single-particle mode). These two simulations together give you the core ideas of quantisation and wave-particle duality in under 15 minutes.
All quantum simulations are accompanied by deep-dive articles in the Learning section, covering the mathematical derivations behind what the simulation shows. The article on the Quantum Harmonic Oscillator covers Hermite polynomials, ladder operators, and the correspondence principle in detail. The full list of quantum simulations is available in the Quantum category.