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arXiv · 2401.15512

Higher energy state approximations in the `Many Interacting Worlds' model

Alex Loomis·Sunder Sethuraman
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Abstract

In the `Many Interacting Worlds' (MIW) discrete Hamiltonian system approximation of Schr\"odinger's wave equation, introduced in \cite{hall_2014}, convergence of ground states to the Normal ground state of the quantum harmonic oscillator, via Stein's method, in Wasserstein-$1$ distance with rate $\mathcal{O}(\sqrt{\log N}/N)$ has been shown in McKeague-Levin (2016), Chen-Thanh (2023), McKeague-Swan (2023). In this context, we construct approximate higher energy states of the MIW system, and show their convergence with the same rate in Wasserstein-$1$ distance to higher energy states of the quantum harmonic oscillator. In terms of techniques, we apply the `differential equation' approach to Stein's method, which allows to handle behavior near zeros of the higher energy states.

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Alex Loomis, Sunder Sethuraman. 2024-01-27. Higher energy state approximations in the `Many Interacting Worlds' model. https://arxiv.org/abs/2401.15512

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