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

2024/01/27 by Loomis, Alex, Sethuraman, Sunder
#60F05 #81Q65 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.15512

Abstract

In the `Many Interacting Worlds' (MIW) discrete Hamiltonian system approximation of Schrödinger's wave equation, introduced in \citehall<sub>2</sub>014, convergence of ground states to the Normal ground state of the quantum harmonic oscillator, via Stein's method, in Wasserstein-1 distance with rate O(√(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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