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RYORAKU is an educational simulation app that allows users to interactively experience the physical phenomena of quantum mechanics.

This is the sixth installment in the series, following SUUGAKU (Mathematics), BUTURAKU (Physics), DENRAKU (Electronics), HARAKU (Waves), and NETURAKU (Thermal Energy). This time, the theme is "Quantum Mechanics." Through 10 simulations, you can learn about the mysteries of quantum mechanics and the beauty of its physical laws while enjoying the experience.

【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 different colors, allowing you to experience the behavior of the wave function by changing the wave number and spread.

▶ Particle in a Box
Visualize the quantized energy levels within an infinite square well potential. Changing the quantum number n changes the number of nodes in the wave function, allowing you to intuitively understand that energy is discrete.

▶ Quantum Tunneling
Simulates how particles pass through a potential barrier using numerical methods to solve the Schrödinger equation. You can observe changes in transmittance by varying the barrier height, width, and particle energy.

▶ Double Slit
Reproduces one of the most famous experiments in quantum mechanics. Simultaneously displays the wave interference pattern and the detection histogram for each particle. Experience how the interference pattern emerges even as particles are detected one by one.

▶ Uncertainty Principle
Visualizes Heisenberg's uncertainty relation (Δx·Δp ≥ ℏ/2) by simultaneously displaying the probability distributions in position space and momentum space. You can intuitively understand that reducing one uncertainty increases the other.

▶ Quantum Entanglement
Reproduces the generation, flight, and measurement of entangled photon pairs with animation. By accumulating correlations while varying the measurement angles of Alice and Bob, you can experimentally confirm the violation of Bell's inequality (CHSH inequality). Experience quantum correlations that exceed the classical limit S=2.

▶ Harmonic Oscillator
Visualize the wave function of a quantum harmonic oscillator using Hermitian polynomials. Display the equally spaced energy levels E_n=ℏω(n+½) and the parabolic potential, allowing for an intuitive understanding of zero-point energy and classical turning points.

▶ Hydrogen Atom
Display the electron orbitals (1s, 2p, 3d…) of a hydrogen atom as a 2D probability density map. Switch between the principal quantum number n, azimuthal quantum number l, and magnetic quantum number m using sliders to observe the orbital shape and radial probability distribution.

▶ Stern-Gerlach Experiment
This experiment recreates the historical experiment where a beam of neutral atoms, when passed through a non-uniform magnetic field, splits into two beams, upper and lower, depending on the spin. Changing the Bloch angle θ alters the measurement probabilities P(↑)=cos²(θ/2) and P(↓)=sin²(θ/2), which are recorded as deposition points on the screen. You can experience spin quantization and projection measurement (Born's law).

▶ Quantum Walk
A quantum version of a random walk. The probability distribution of a quantum particle repeatedly performing Hadamard coin operations and shift operations is displayed simultaneously with that of a classical random walk. While the classical walk spreads in a normal distribution (diffusion ∝√t), the quantum walk creates a bimodal distribution through interference and spreads linearly (ballistic ∝t). The difference can be compared at a glance.

【Features】
• Real-time parameter adjustment available for all simulations
• Real-time display of physical formulas and numerical values
• Dark mode / Light mode support
• Intuitive and beautiful UI
• Ads are limited to banners at the bottom of the screen

【Recommended for】
• Students studying quantum mechanics in physics classes
• Those who want to intuitively understand the quantum world
• Teachers who want to use it as teaching material
• Anyone interested in quantum mechanics