An interactive quantum mechanics visualization tool that solves and animates the time-dependent Schrödinger equation for various potential configurations.
- Time-dependent Schrödinger equation solver using the split-operator method
- Real-time wavefunction evolution with customizable time steps
- Multiple potential types including harmonic oscillator, infinite/finite square wells, step potentials, barriers, and double wells
- Various initial states including Gaussian wave packets, energy eigenstates, superposition states, and coherent states
- Wavefunction plotting showing real and imaginary components
- Probability density visualization with filled area plots
- Phase space representation for momentum-position analysis
- Energy spectrum display for eigenstate analysis
- Real-time animation of quantum evolution
- Expectation values for position ⟨x⟩ and momentum ⟨p⟩
- Uncertainty calculations (Δx, Δp) with Heisenberg uncertainty principle verification
- Total energy computation including kinetic and potential components
- Normalization verification for quantum state validity
- Futuristic aurora-themed design with gradient animations
- Responsive layout optimized for desktop and tablet viewing
- Interactive controls with real-time parameter adjustment
- Tabbed visualization interface for different quantum observables
- Loading animations with quantum orbital effects
- Split-operator technique for time evolution
- Fast Fourier Transform (FFT) for momentum space calculations
- Finite difference methods for spatial derivatives
- Normalized wavefunctions ensuring quantum probability conservation
- Harmonic Oscillator: V(x) = ½mω²x²
- Infinite Square Well: V(x) = ∞ for |x| > L/2
- Finite Square Well: V(x) = V₀ for |x| > L/2
- Step Potential: V(x) = V₀ for x > 0
- Potential Barrier: V(x) = V₀ for |x| < a/2
- Double Well: Custom double-well configuration
- Gaussian Wave Packet: Localized state with definite position/momentum
- Energy Eigenstate: Stationary states with definite energy
- Superposition: Linear combination of multiple eigenstates
- Coherent State: Quantum harmonic oscillator coherent states
- Open
index.htmlin a modern web browser - Select your desired potential type from the dropdown
- Configure initial conditions (position, momentum, wave packet width)
- Adjust potential parameters (frequency, well width, barrier height, etc.)
- Click "Solve Equation" to generate the quantum solution
- Use the time evolution slider to animate the wavefunction
- Potential Type: Choose from 6 different quantum potentials
- Initial State: Select Gaussian, eigenstate, superposition, or coherent state
- Energy Level (n): For eigenstate calculations (1-10)
- Initial Position (x₀): Starting position of the wave packet
- Initial Momentum (p₀): Initial momentum of the particle
- Wave Packet Width (σ): Spatial spread of the initial state
- Particle Mass (m): Effective mass of the quantum particle
- Evolution Time: Real-time animation control (0-20 time units)
- Wavefunction: Real and imaginary parts of ψ(x,t)
- Probability Density: |ψ(x,t)|² probability distribution
- Phase Space: Momentum-position representation
- Energy Spectrum: Energy eigenvalue analysis
- Modern browsers with ES6+ support
- WebGL capability for smooth animations
- Plotly.js for scientific plotting
- Plotly.js (v2.27.0) - Loaded via CDN
- No additional installation required
- Optimized for 512-point spatial grids
- Real-time FFT calculations
- Efficient split-operator time evolution
- Smooth 60fps animations
- Wave-particle duality visualization
- Heisenberg uncertainty principle demonstration
- Quantum tunneling through potential barriers
- Energy quantization in bound systems
- Superposition and interference effects
- Undergraduate quantum mechanics
- Advanced physics laboratories
- Computational physics demonstrations
- Research visualization tool
This simulation implements the full time-dependent Schrödinger equation:
iℏ ∂ψ/∂t = Ĥψ = [-ℏ²/2m ∇² + V(x)]ψ
The numerical methods are research-grade and suitable for:
- Educational demonstrations
- Preliminary research calculations
- Method development and testing
- Quantum algorithm prototyping
- Chrome/Safari/Firefox: Latest versions recommended
- JavaScript: ES6+ support required
- WebGL: For optimal rendering performance
- Screen Resolution: 1024x768 minimum, 1920x1080+ recommended
This project is open source and available for educational and research purposes.
Experience quantum mechanics through interactive visualization and real-time simulation.