PreprintCC BY 4.0arXiv
Tunneling from an oscillating state in quantum mechanics
Abstract
We study the decay of general initial states out of a metastable potential well in quantum mechanics. We provide a closed-form expression for the probability current that tunnels through the barrier in terms of the resonant states into which the initial state can be decomposed. All ingredients are computed analytically to first subleading order in the semiclassical limit. Specializing to a coherently-oscillating state, we derive an equivalent semiclassical approximation to the current via the path integral, which circumvents the decomposition into resonant states. We test the accuracy of the approximation by comparing it to a numerical solution of the Schrödinger equation.
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BibTeX
@misc{janssen2026tunneling,
title = {{Tunneling from an oscillating state in quantum mechanics}},
author = {Oliver Janssen and Matthew Kleban and Cameron Norton},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.04139},
eprint = {2605.04139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04139},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tunneling from an oscillating state in quantum mechanics
AU - Oliver Janssen
AU - Matthew Kleban
AU - Cameron Norton
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2605.04139
UR - https://arxiv.org/abs/2605.04139
AB - We study the decay of general initial states out of a metastable potential well in quantum mechanics. We provide a closed-form expression for the probability current that tunnels through the barrier in terms of the resonant states into which the initial state can be decomposed. All ingredients are computed analytically to first subleading order in the semiclassical limit. Specializing to a coherently-oscillating state, we derive an equivalent semiclassical approximation to the current via the path integral, which circumvents the decomposition into resonant states. We test the accuracy of the approximation by comparing it to a numerical solution of the Schrödinger equation.
ER -