The Uncertainty Principle in Terms of Isoperimetric Inequalities

• 作者: Thomas Schürmann
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: UNCERTAINTY PRINCIPLE DIRICHLET EIGENVALUE Wirtinger INEQUALITY
• 年，卷（期）: 2017,（3）
• 页码范围: 307-311
• 页数: 5页
• 分类号: O1

摘要

Simultaneous measurements of position and momentum are considered in n dimensions. We find, that for a particle whose position is strictly localized in a compact domain (spatial uncertainty) with non-empty boundary, the standard deviation of its momentum is sharply bounded by , while is the first Dirichlet eigenvalue of the Laplacian on D.