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

TL;DR

The paper introduces 1d-qt-ideal-solver, an open-source Python library for simulating idealized 1D quantum tunneling with high fidelity, validated through canonical test cases and suitable for educational and qualitative research purposes.

Contribution

It presents a novel, efficient, and accessible Python implementation of a quantum tunneling solver using spectral methods and absorbing boundaries, validated against canonical models.

Findings

Rectangular barriers show higher transmission than Gaussian barriers in over-barrier regime.

Simulations maintain machine-precision energy conservation over femtosecond timescales.

Phase space analysis indicates complete decoherence in averaged conditions.

Abstract

We present 1d-qt-ideal-solver, an open-source Python library for simulating one-dimensional quantum tunneling dynamics under idealized coherent conditions. The solver implements the split-operator method with second-order Trotter-Suzuki factorization, utilizing FFT-based spectral differentiation for the kinetic operator and complex absorbing potentials to eliminate boundary reflections. Numba just-in-time compilation achieves performance comparable to compiled languages while maintaining code accessibility. We validate the implementation through two canonical test cases: rectangular barriers modeling field emission through oxide layers and Gaussian barriers approximating scanning tunneling microscopy interactions. Both simulations achieve exceptional numerical fidelity with machine-precision energy conservation over femtosecond-scale propagation. Comparative analysis employing information-theoretic measures and nonparametric hypothesis tests reveals that rectangular barriers exhibit moderately higher transmission coefficients than Gaussian barriers in the over-barrier regime, though Jensen-Shannon divergence analysis indicates modest practical differences between geometries. Phase space analysis confirms complete decoherence when averaged over spatial-temporal domains. The library name reflects its scope: idealized signifies deliberate exclusion of dissipation, environmental coupling, and many-body interactions, limiting applicability to qualitative insights and pedagogical purposes rather than quantitative experimental predictions. Distributed under the MIT License, the library provides a deployable tool for teaching quantum mechanics and preliminary exploration of tunneling dynamics.