基于半正定优化的共形自举方法在量子力学中的应用
The Application of Conformal Bootstrap Method Based on Semi-Definite Programming in Quantum Mechanics
DOI: 10.12677/pm.2024.144118, PDF,    国家自然科学基金支持
作者: 张会鹏, 李卓然, 樊 炜：江苏科技大学理学院，江苏 镇江
关键词: 半正定优化；Numerical Bootstrap；量子非谐振子；Semi-Definite Programming； Numerical Bootstrap； Quantum Anharmonic Oscillator
摘要: 半正定优化是一种非常重要的数学方法，有着广泛的应用。最近两年的研究表明，半正定优化可以用来求解量子力学中的非谐振子问题。本文对此展开研究，以一个一般的多项式势函数为例，表明半正定优化可以求解量子力学中具有一般多项式形式的势函数问题。本文介绍如何将量子力学问题转化为半正定优化问题，并给出数值结果。
Abstract: The semi-definite programming is a very important mathematical method with a wide range of applications. Recent studies in the last two years have shown that the semi-definite programming can be used to solve quantum anharmonic oscillators. In this paper, we study a quantum problem with a general polynomial potential. We describe how to transform a quantum mechanical problem into a semi-definite programming problem and gives numerical results. The results show that this method can be used to solve quantum mechanical problems with a general polynomial potential.
文章引用：张会鹏, 李卓然, 樊炜. 基于半正定优化的共形自举方法在量子力学中的应用[J]. 理论数学, 2024, 14(4): 119-125. https://doi.org/10.12677/pm.2024.144118

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