QuantumLab: Research-Grade Quantum Simulation Framework

A high-performance, modular Python library for numerical quantum mechanics simulations. QuantumLab solves the 1D Time-Dependent Schrödinger Equation (TDSE) using the Split-Step Fourier Method (SSFM) to model quantum wave packet dynamics with high physical fidelity.

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Key Features

• Unitary Time-Step Solver: High-precision split-step solver conserving the total probability norm to machine precision ($< 10^{-12}$).
• Physical Observables Module: Real-time evaluation of expectation values ($\langle x \rangle$, $\langle p \rangle$, $\langle E \rangle$, $\langle T \rangle$, $\langle V \rangle$) and quantum uncertainties ($\Delta x$, $\Delta p$) proving Heisenberg's uncertainty principle.
• Modular Potential Registry:
  • Barriers: Gaussian, Rectangular, Step, Multiple, and Resonant Tunneling Diodes (RTD).
  • Wells: Infinite Square Well, Finite Square Well, and quartic Double Well.
  • Oscillators: Harmonic Oscillator.
  • Periodic: Sine-squared lattice (Crystal Potential).
  • Disorder: Cell-based random potential for Anderson localization.
  • Custom: User-defined Python callable functions.
• Aesthetic Plotting: Publication-ready scientific plotting with LaTeX markup, custom typography, light/dark themes, and dual-space (position and momentum side-by-side) analyses.
• 3D Space-Time Rendering: Premium 3D surface visualizations of probability density evolution.

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Example Gallery

The framework includes pre-built simulation scripts under the examples/ directory. Each example generates scientific visualizations:

1. Gaussian Barrier Scattering (examples/01_gaussian_barrier.py)

Propagates a wave packet towards a Gaussian potential barrier, resolving reflection ($R$) and transmission ($T$) coefficients.

• Final State Plot:
• 3D Space-Time Surface:
• Dual Space Analysis:

2. Harmonic Oscillator (examples/02_harmonic_oscillator.py)

Simulates a coherent state wave packet oscillating back and forth in a parabolic well, demonstrating exact total energy conservation.

• Final State Plot:
• 3D Space-Time Surface:

3. Double Well Tunneling (examples/03_double_well.py)

Illustrates quantum tunneling and wave packet oscillations between two symmetric wells separated by a central potential barrier.

• Final State Plot:
• 3D Space-Time Surface:

4. Multiple Barrier Scattering (examples/04_multiple_barriers.py)

Models wave packet splitting and high-frequency interference fringes as the packet scatters off multiple rectangular barriers.

• Final State Plot:
• 3D Space-Time Surface:

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Installation & Usage

1. Install Dependencies

Install QuantumLab in development/editable mode:

pip install -e .

2. Run Simulations

Run any example script directly:

python examples/01_gaussian_barrier.py
python examples/02_harmonic_oscillator.py
python examples/03_double_well.py
python examples/04_multiple_barriers.py

3. Run Verification Tests

Execute the unit test suite to verify physical accuracy and energy conservation:

pytest tests/ -v