Marching toward the eigenvalues: The Canonical Function Method and the Schrödinger equation

A Nonperturbative Perspective on Inner Product Quantization: Highly Accurate Solutions to the Schr{ö}dinger Equation

We devise a new and highly accurate quantization procedure for the inner product representation, both in configuration and momentum space. Utilizing the representation $Ψ(ξ) = \sum_{i}a_i[E]ξ^i R_β(ξ)$, for an appropriate reference function, $R_β(ξ)$, we demonstrate that the (convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the exact bound/resonance state energies with increasing accuracy as $i \to \infty$. The validity of the approach is shown to be based on an extension of the Hill determinant quantization procedure. Our method has been applied, with remarkable succ…

对数薛定谔方程的小时间近似可控性

Small-time approximate controllability of the logarithmic Schr\''dinger equation

该论文证明了对数非线性薛定谔方程在双线性控制下的小时间全局近似可控性，通过结合相位控制和梯度流方法，并借助WKB分析处理非线性估计，为首个此类结果。

分钟级自旋5/2原子的薛定谔猫态

Minutes-scale Schr{ö}dinger-cat state of spin-5/2 atoms

本研究展示了光阱中自旋5/2镱原子的长寿命薛定谔猫态，相干时间达1400秒，并利用拉姆齐干涉法实现海森堡极限计量，为量子精密测量提供新方案。

The Schr$\ddot{o}$dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics

In this paper it is argued how the dynamics of the classical Newtonian N-body system can be described in terms of the Schr$\ddot{o}$dinger-Poisson equations in the large $N$ limit. This result is based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. According to the Calogero conjecture, the emerging effective Planck constant is computed in terms of the parameters of the N-body system as $\hbar \sim M^{5/3} G^{1/2} (N/<ρ>)^{1/6}$, where is $G$ the gravitational constant, $N$ and $M$ are the number and the mass of the bodies, and $<ρ>$ is their average densit…