Energy spectrum of a constrained quantum particle and the Willmore energy of the constraining surface

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Vicent Gimeno i Garcia, Steen Markvorsen
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引用次数: 0

Abstract

In this paper, we establish geometric and topological upper bounds on the first energy level gap of a particle confined to move on a compact surface in $3$-space. Our main contribution is proving that the first gap in the energy spectrum of a confined particle (a physical property) is bounded above by the Willmore energy of the confining surface (a geometric property). Furthermore, we demonstrate that the only surfaces that permit a confined particle with a stationary and uniformly distributed wave function are surfaces with constant skew curvature.
受约束量子粒子的能谱和约束面的威尔摩尔能
在本文中,我们建立了在 3 美元空间的紧凑表面上受限运动的粒子的第一能级间隙的几何和拓扑上限。我们的主要贡献在于证明了受限粒子能谱中的第一能级间隙(物理特性)受限于受限表面的威尔摩尔能(几何特性)。此外,我们还证明了只有具有恒定倾斜曲率的曲面才允许受限粒子具有静止且均匀分布的波函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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