1d-qt-ideal-solver 0.0.1

Simplified 1D quantum tunneling solver with 4 classic test cases

1d-qt-ideal-solver: Idealized 1D Quantum Tunneling Solver

High-performance 1D quantum tunneling solver implementing the split-operator Fourier method with adaptive time stepping, Numba-accelerated parallel computation, and optional stochastic noise for idealized simulations of coherent tunneling dynamics in nanoscale barrier systems.

Physics

Solves the time-dependent Schrödinger equation in natural units ($\hbar = m_e = 1$):

$$i\frac{\partial \psi}{\partial t} = \hat{H}\psi = \left[-\frac{1}{2}\nabla^2 + V(x,t)\right]\psi$$

The wavefunction evolves via the split-operator method:

$$\psi(x, t+\delta t) = e^{-iV\delta t/2} \cdot \mathcal{F}^{-1}\left[e^{-ik^2\delta t/2}\mathcal{F}[\psi]\right] \cdot e^{-iV\delta t/2}$$

Key Observables:

• Transmission coefficient: $T = \int_{x>x_b} |\psi(x,t_f)|^2 dx$
• Reflection coefficient: $R = \int_{x<x_a} |\psi(x,t_f)|^2 dx$
• Unitarity: $T + R \approx 1$

Features

• Adaptive Time Stepping: Automatically adjusts $\delta t$ based on wavefunction dynamics
• Numba JIT Compilation: 10-100× speedup via parallel CPU execution
• Stochastic Environments: Ornstein-Uhlenbeck noise ($\tau_{\text{corr}}$) and decoherence ($\gamma$)
• Conservation Monitoring: Real-time validation of $|\psi|^2 = 1$ and energy conservation
• Professional Visualization: Parallel-rendered GIF animations with publication-quality aesthetics
• NetCDF4 Output: Self-describing, compressed data format for reproducible research

Installation

From PyPI:

pip install 1d-qt-ideal-solver

From source:

git clone https://github.com/yourusername/1d-qt-ideal-solver.git
cd 1d-qt-ideal-solver
pip install -e .

Quick Start

Command-line interface:

# Run individual test case
qt1d-simulate case1                    # Rectangular barrier
qt1d-simulate case2 --cores 8          # Double barrier (8 cores)

# Run all 4 cases sequentially
qt1d-simulate --all

# Custom configuration
qt1d-simulate --config myconfig.txt

Python API:

from qt1d_ideal import QuantumTunneling1D, GaussianWavePacket

# Initialize solver
solver = QuantumTunneling1D(nx=2048, x_min=-10, x_max=10)

# Prepare initial Gaussian wave packet
psi0 = GaussianWavePacket(x0=-5.0, k0=5.0, sigma=0.5)(solver.x)

# Define rectangular barrier: V₀ = 2 eV, width = 2 nm
V = solver.rectangular_barrier(height=2.0, width=2.0)

# Solve dynamics
result = solver.solve(
    psi0=psi0, 
    V=V, 
    t_final=5.0,
    n_snapshots=200,
    noise_amplitude=0.05,      # 50 meV stochastic noise
    decoherence_rate=0.001     # T₂ ≈ 1 ps
)

print(f"T = {result['transmission_coefficient']:.2%}")
print(f"R = {result['reflection_coefficient']:.2%}")

Output Files

Simulation data (in outputs/):

• *.nc — NetCDF4 format (wavefunction evolution, parameters, metadata)
• *.gif — High-quality animations with statistics overlay

Diagnostics (in logs/):

• *.log — Complete simulation records with conservation diagnostics

Physical Applications

Relevant for idealized studies of quantum tunneling in:

• Nuclear Physics: α-decay (fm scale)
• Surface Science: STM imaging, field emission (Å scale)
• Chemical Dynamics: Proton transfer reactions (nm scale)
• Nanoelectronics: Resonant tunneling diodes, Josephson junctions (μm scale)

Performance

• Runtime: 10-30 seconds per case (2048 grid points, 200 frames)
• Parallel Rendering: ~10× faster GIF generation via multiprocessing
• Accuracy: Norm error < 0.1%, energy conservation < 1%

Citation

If you use this solver in your research, please cite:

@software{qt1d_solver_2025,
  author = {Kaban, Siti N. and Herho, Sandy H. S. and Prayogo, Sonny and Anwar, Iwan P.},
  title = {1D Quantum Tunneling Solver: Idealized Split-Operator Method},
  year = {2025},
  version = {0.0.1},
  url = {https://github.com/yourusername/1d-qt-ideal-solver},
  license = {MIT}
}

Authors

• Siti N. Kaban
• Sandy H. S. Herho ([e-mail])
• Sonny Prayogo
• Iwan P. Anwar

License

MIT License — See LICENSE for details.