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arXiv · 2605.17395

Time dependent Schr\"odinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field

Jiyu Fan·Ari Laptev
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Abstract

We construct an approximation of the kernel of the solution of the time dependent Schr\"odinger equation whose Hamiltonian is a 2D harmonic oscillator in Aharonov-Bohm magnetic field. The main tools used here were established in the paper of A. Laptev and I.M. Sigal, where the authors considered a class of Fourier Integral Operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schr\"odinger equations. For the example considered in this paper we are able to find the main term in the approximation of the kernel that equals a version of the Mehler formula.

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Jiyu Fan, Ari Laptev. 2026-05-17. Time dependent Schr\"odinger equation for harmonic oscillator in the Aharonov-Bohm magnetic field. https://arxiv.org/abs/2605.17395

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