Simulating Atom

Made by andrebuilds

A collection of interactive hydrogen atom physics simulators, written in C++ with OpenGL/GLFW/GLM and Python.

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Project Files

atom.cpp

2D multi-atom simulation with electromagnetic waves

Displays 20 atoms arranged in a circle that repel each other. Each atom has a proton and an orbiting electron. Left-clicking the mouse emits 25 waves in all directions, which can excite electrons (quantum level jump n). When an electron decays back, it emits a wave in return.

Physics implemented:

• Circular orbits for discrete energy levels (Bohr model)
• Bohr energy: $E_n = -13.6/n^2$ eV
• Photon absorption and emission for energy transitions
• Inter-atom repulsion force + boundary repulsion

Where to improve:

• Engine is a global singleton — better to pass it as a parameter or use dependency injection
• The O(N²) loop for wave-electron collisions is very slow with many atoms/waves: using a spatial hash grid would reduce complexity
• Wave energy comparison uses exact float equality (wave.energy == energyforUp) — very fragile, should use abs(a-b) < epsilon
• a.pos += a.v is commented out: atom movement is disabled
• Waves with energy == 0.0f are never removed from memory, only skipped: wastes memory over time

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wave_atom_2d.cpp

2D single-atom simulation with wavy orbits

A more artistic/visual version of a single atom. The electron orbit is not circular but wavy — the radius oscillates as a sine function, where the number of oscillations is determined by the particle's energy. The user can raise/lower the energy with keys W/S, E/D, R/F.

Physics implemented:

• Orbit with modulated radius: $r(\theta) = r_0 + A \cdot \sin(n_{osc} \cdot \theta)$
• Number of oscillations proportional to $-13.6 / E$, echoing quantum numbers

Where to improve:

• numOscillations is computed twice in both draw() and update() — should be saved as a struct member
• No fixed delta-time in the loop: simulation speed depends on the monitor FPS
• amplitude = 50.0f and baseOrbit = 200.0f are hardcoded magic values
• Energy can go positive (ionized particle) without any edge case handling

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atom_realtime.cpp

3D real-time quantum orbital viewer with probability current physics

The most advanced program in the collection. It samples the real hydrogen wave function $\psi_{n,l,m}(r,\theta,\phi)$ using CDF sampling for $r$ and $\theta$, distributing N particles in 3D space according to the probability density $|\psi|^2$. Particles are then animated according to the probability current $\vec{j} \propto \hbar m / (m_e r \sin\theta)$.

Rendering uses modern GLSL shaders (vertex/fragment), VAO/VBO, perspective projection and a mouse-controlled orbital camera.

Physics implemented:

• Associated Laguerre polynomials for the radial part
• Associated Legendre polynomials for $\theta$
• Probability current for electron motion
• "Fire" heatmap coloring based on speed/distance

Where to improve:

• sampleR and sampleTheta use static variables with built = false: does NOT work if n, l, m are changed at runtime — the CDF is never rebuilt. Must invalidate it when parameters change
• Sampling runs on a single thread: parallelizing with std::async or a thread pool would drastically reduce loading times for large N
• All parameters (n, l, m, N) are globals: better to encapsulate them in a config struct
• The shader is hardcoded as a C++ string — better to load it from an external .glsl file
• vec3 vel in the Particle struct does not appear to be used consistently with the declared physics

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atom_raytracer.cpp

3D orbital viewer with software ray tracing for spheres

Similar to atom_realtime.cpp for the physics sampling, but uses ray tracing to render each particle as a lit sphere. For each screen pixel a ray is cast and sphere intersections are computed, producing physically accurate shading and highlights. Uses an "inferno" colormap to map probability density to color.

Physics implemented:

• Same quantum sampling as atom_realtime.cpp
• Ray-sphere intersection for every particle
• Sphere normal shading with a point light source

Where to improve:

• Ray tracing is CPU-bound and O(pixels × particles): with 100,000 particles and 800×600 pixels it is impractical without optimization. A BVH (Bounding Volume Hierarchy) would reduce complexity from O(N) to O(log N) per ray
• The render loop is single-threaded: splitting pixel rows across threads with std::thread or OpenMP would give linear speedup with core count
• Same static CDF bug as in atom_realtime.cpp
• LightingScaler = 700 is a hardcoded magic value

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schrodinger.py

Python generator for complex wave function samples

Python script that generates samples of the complex wave function $\psi_{n,l,m}$ using rejection sampling, and saves them as JSON in the orbitals/ folder. Samples include the 3D position and the complex $\psi$ value (real and imaginary parts). The generated JSON can be loaded into the C++ viewers.

Where to improve:

• Uses rejection sampling (very inefficient for high n states): better replaced with CDF sampling as in the C++ files
• max_prob is updated on-the-fly during sampling: this introduces a statistical bias since early samples use an underestimated threshold. Better to do a pre-pass to find max_prob
• No progress bar for large N: add tqdm
• JSON files can become very large (hundreds of MB for N=100000): consider a binary format like numpy .npy

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mesh.json

JSON file containing a 3D mesh (vertices), likely generated by schrodinger.py or an external tool, used as input by one of the C++ viewers.

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Dependencies

Library	Purpose
GLEW	OpenGL extension loading
GLFW3	Window creation and input handling
GLM	Vector/matrix math
Python 3 + numpy, scipy	Only for schrodinger.py

Building (Windows with vcpkg)

# Install dependencies
C:\vcpkg\vcpkg install glew glfw3 glm

# Build from VS Code command palette
Ctrl+Shift+P → Run Task → choose the file to compile

Controls

Program	Key / Action	Effect
atom.exe	Left click	Emits 25 photon waves
wave_atom_2d.exe	W / S	Increase / decrease energy (×0.01)
wave_atom_2d.exe	E / D	Increase / decrease energy (×0.1)
wave_atom_2d.exe	R / F	Increase / decrease energy (×1.0)
atom_realtime.exe	Mouse drag	Rotate orbital camera
atom_raytracer.exe	Mouse drag	Rotate orbital camera

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Made by andrebuilds