论文标题
Schrödinger方程的反问题的半古典限制
Semi-classical limit of an inverse problem for the Schrödinger equation
论文作者
论文摘要
经典的推导是，源自包含量子信息的schrödinger方程的Wigner方程在重新缩放的Planck常数$ε\ to0 $时收敛到liouville方程。由于后者提出了牛顿的第二定律，因此该过程通常被称为（半）经典限制。在本文中，我们研究了Schrödinger方程的反问题的经典限制。更具体地说，我们表明，使用Schrödinger方程的初始条件和最终状态重建潜在项，在具有$ε\ to0 $的经典制度中，使用初始和最终状态来重建Liouville方程中的潜在术语。这正式桥接了量子力学中的一个反问题，与经典力学中的问题相反。
It is a classical derivation that the Wigner equation, derived from the Schrödinger equation that contains the quantum information, converges to the Liouville equation when the rescaled Planck constant $ε\to0$. Since the latter presents the Newton's second law, the process is typically termed the (semi-)classical limit. In this paper, we study the classical limit of an inverse problem for the Schrödinger equation. More specifically, we show that using the initial condition and final state of the Schrödinger equation to reconstruct the potential term, in the classical regime with $ε\to0$, becomes using the initial and final state to reconstruct the potential term in the Liouville equation. This formally bridges an inverse problem in quantum mechanics with an inverse problem in classical mechanics.
