We present the case of quantal transmission through a smooth, single-piece exponential potential, $V(x)=-V_0 e^{x/a}$, in contrast to the piece-wise continuous potentials, as a pedagogic model to demonstrate the analytic extraction of transmission (reflection) co-efficient.

2003-09-24quant-ph

Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation

The Schr{ö}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schr{ö}dinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and the su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant se…

2007-09-10quant-ph

Wavefunction collapse induced by gravity in a relativistic Schr{\''o}dinger-Newton model

A relativistic version of the Schr{ö}dinger-Newton equation is analyzed within the recently proposed Grave de Peralta approach [L. Grave de Peralta, {\em Results Phys.} {\bf 18} (2020) 103318], which include relativistic effects by a parametrization of the non-relativistic hamiltonian, so as to impose that the average kinetic energy of the system coincide with its relativistic kinetic energy. The reliability of this method is tested for the particle in a box. By applying this method to the Schr{ö}dinger-Newton equation we shows that the characteristic length of the model [L. Di{ó}si, {\em Phys…

2021-02-11quant-ph

Straightforward Derivation of the Schr{ö}dinger Equation from Classical Mechanics and the Planck Postulate

According to the widely accepted notion, the Schr{ö}dinger equation (SE) is not derivable in principle. Contrary to this belief, we present here a straightforward derivation of SE. It is based on only two fundamentals of mechanics: the classical Hamilton-Jacobi equation(HJE) and the Planck postulate about the discrete transfer of energy at micro-scales. Our approach is drastically different from the other published derivations of SE which either employ an ad hoc underlying assumption about the probabilistic or the statistical nature of the micro-scale phenomena, or rely on the prior knowledge …

2008-04-16quant-ph

Implementation of traveling odd Schr$ö$dinger cat states in circuit-QED

We propose a realistic scheme of generating a traveling odd Schr$ö$dinger cat state and a generalized entangled coherent state in circuit quantum electrodynamics (circuit-QED). A squeezed vacuum state is used as initial resource of nonclassical states, which can be created through a Josephson traveling-wave parametric amplifier, and travels through a transmission line. Because a single-photon subtraction from the squeezed vacuum gives with very high fidelity an odd Schr$ö$dinger cat state, we consider a specific circuit-QED setup consisting of the Josephson amplifier creating the traveling res…

2016-10-27quant-ph

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…

1997-07-02quant-ph

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Web-Schrödinger: Program for the interactive solution of the time dependent and stationary two dimensional (2D) Schr{ö}dinger equation

Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or mi…

2020-04-18physics.comp-phphysics.ed-phquant-ph

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。

2024-10-12physics.atom-phquant-ph

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。

2025-10-16math-phmath.APmath.MP

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…

2017-09-18astro-ph.COgr-qcnlin.CD