Quantum Physics

Quantum physics is the branch of physics that describes matter and energy at the smallest scales — electrons, photons and atoms — where the intuitions built from everyday objects stop working. A particle can behave like a wave, a wave can behave like a particle, and a system can exist in a superposition of several states until it is measured. This hub gathers every interactive quantum simulation on mysimulator.uk into one guided starting point, so instead of reading equations on a page you can drag a slider, watch a wavefunction evolve, and see the strange predictions of quantum theory play out in real time in your browser.

The historical core of the topic is wave-particle duality, demonstrated most famously by the double-slit experiment: send particles one at a time through two narrow slits and an interference pattern still builds up on the screen, as if each particle passed through both slits at once. The Heisenberg uncertainty principle formalises a related limit — a particle's position and momentum can never both be known with arbitrary precision, no matter how good the measuring equipment is. The Schrödinger equation simulation lets you solve the underlying wave equation numerically with the split-operator method, watching a Gaussian wave packet spread, reflect and tunnel through potential barriers exactly as the mathematics predicts.

Quantum tunnelling is one of the most consequential of these effects: a particle can cross an energy barrier it does not classically have enough energy to climb, with a transmission probability that depends exponentially on the barrier's height and width. The same mathematics that describes tunnelling through a rectangular barrier also explains scanning tunnelling microscopes, flash memory, and the fusion reactions that power stars. The hydrogen orbital simulation applies the same wave-mechanics toolkit to a real atom, rendering the exact probability densities |ψₙₗₘ|² that chemists use to predict molecular bonding geometry — the shapes are not illustrations, they are the actual solutions of the Schrödinger equation for a single electron bound to a proton.

The second half of this hub moves from quantum mechanics to quantum computing, where a qubit's state is a point on the Bloch sphere rather than a single classical bit. The quantum circuit simulator lets you place Hadamard, Pauli and CNOT gates to build real algorithms — a Bell state, a GHZ state, or a two-qubit Grover search that finds a marked item faster than any classical algorithm can. Bell's Inequality and the entanglement simulation demonstrate why this speed-up is possible: measuring one entangled qubit instantly determines the outcome for its partner, and the correlations violate the CHSH inequality in a way no classical hidden-variable theory can reproduce. BB84 shows the same entanglement-free superposition trick used defensively, in quantum key distribution, where any eavesdropper's measurement necessarily disturbs the qubits and reveals itself as a raised error rate.

Together these simulations cover the two pillars of modern quantum science: the wave mechanics that explains atoms, lasers and semiconductors, and the qubit mechanics behind quantum computing and quantum cryptography. Follow the learning path below for a suggested order, browse the full grid for anything that catches your eye, or jump straight to the category pages for Quantum Physics and Quantum Computing for the complete lists.

What makes these simulations different from a textbook diagram is that every one of them is a real numerical solver running live in your browser, not a pre-rendered animation. The Schrödinger equation simulation genuinely integrates the split-operator method frame by frame, so changing the barrier height or the initial momentum changes the physics, not just the picture — you can push a wave packet's energy above and below a barrier and watch the transmission coefficient respond exactly as the WKB approximation predicts. The quantum circuit simulator genuinely multiplies the state vector through your chosen sequence of gate matrices, so building a GHZ state or a two-qubit Grover search produces the same probability histogram a real quantum processor would report, within the limits of the simplified noise model. That distinction matters for students preparing for exams, for teachers building a lesson around a single adjustable parameter, and for anyone who wants an intuition for quantum mechanics that survives contact with the real equations — because the numbers on screen are the numbers the mathematics actually produces, not an artist's impression of them.