RYORAKU

RYORAKU is an interactive educational simulation app that lets you experience quantum mechanics phenomena hands-on.

Explore 10 beautifully visualized simulations and discover the mysteries and elegance of quantum physics.

【10 Simulations】

▶ Wave Function
Observe the time evolution of a Gaussian wave packet in real time. The real part, imaginary part, and probability density are displayed in distinct colors. Adjust the wave number and spread to see how the wave function behaves.

▶ Particle in a Box
Visualize quantized energy levels inside an infinite square well potential. Change the quantum number n to see how the number of nodes changes and understand that energy is discrete.

▶ Quantum Tunneling
Simulate a particle penetrating a potential barrier using numerical solutions of the Schrödinger equation. Vary the barrier height, width, and particle energy to observe changes in transmission probability.

▶ Double Slit
Recreate the most famous experiment in quantum mechanics. See the wave interference pattern and particle-by-particle detection histogram simultaneously. Watch as an interference pattern emerges even when particles are detected one at a time.

▶ Uncertainty Principle
Display position-space and momentum-space probability distributions side by side, visualizing Heisenberg's uncertainty relation (Δx·Δp ≥ ℏ/2). See how reducing uncertainty in one quantity increases it in the other.

▶ Quantum Entanglement
Watch entangled photon pairs being created, flying apart, and being measured with real-time animation. Adjust Alice and Bob's measurement angles to accumulate correlations and experimentally confirm the violation of Bell's inequality (CHSH). Experience quantum correlations that exceed the classical limit of S=2.

▶ Harmonic Oscillator
Visualize the quantum harmonic oscillator wave functions using Hermite polynomials. See equally spaced energy levels E_n=ℏω(n+½), the parabolic potential, and understand zero-point energy and classical turning points intuitively.

▶ Hydrogen Atom
Display hydrogen atom electron orbitals (1s, 2p, 3d…) as 2D probability density maps. Switch between principal quantum number n, angular momentum l, and magnetic quantum number m with sliders to observe orbital shapes and radial probability distributions.

▶ Stern-Gerlach
Recreate the historic 1922 experiment where a beam of neutral atoms passing through an inhomogeneous magnetic field splits into two discrete spots according to spin. Adjust the input Bloch angle θ to control measurement probabilities P(↑)=cos²(θ/2), P(↓)=sin²(θ/2), and watch the screen accumulate spin-up and spin-down deposits — a hands-on demonstration of spin quantization and the Born rule.

▶ Quantum Walk
The quantum analogue of the random walk. A particle alternates Hadamard coin operations and position shifts, while the classical random walk is shown side by side. Compare the bimodal, ballistically spreading quantum distribution (σ ∝ t) with the diffusive Gaussian classical distribution (σ ∝ √t) at every step.

【Features】
• Adjust parameters in real time across all simulations
• Physics formulas and values displayed in real time
• Dark mode / Light mode support
• Intuitive and beautiful UI
• Only a small banner ad at the bottom

【Who is this for?】
• Students studying quantum mechanics in physics class
• Anyone who wants to intuitively understand the quantum world
• Teachers looking for classroom tools
• Anyone curious about quantum mechanics