自旋为1/2粒子的相对论量子定态Hamilton Jacobi方程

从Hamilton-Jacobi方程导出含时薛定谔方程

Time-dependent Schrödinger equation from the Hamilton-Jacobi equation

这篇论文和摘要已被撤回。

广义Hamilton-Jacobi表象描述薛定谔波函数微观态的位置和原因

Where and why the generalized Hamilton-Jacobi representation describes microstates of the Schrödinger wave function

广义哈密顿-雅可比表示描述了束缚态薛定谔波函数的微观态。在边界值应用于束缚态薛定谔波函数的点处，量子力学的广义哈密顿-雅可比方程表现出节点奇异性。对于初值问题，这两种表示是等价的。

PT对称哈密顿量的量子Hamilton-Jacobi分析

Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians

我们应用量子Hamilton-Jacobi形式主义，自然地定义在复杂的域中，一些复杂的哈密顿量，其特征在于离散宇称和时间反转（PT）对称性，并获得其本征值和本征函数。分析了准精确可解势和精确可解势的例子，指出了它们的量子动量函数在奇异性结构上的细微差别。PT对称性在复域中的作用也被说明。

Solutions of the Schrödinger equation given by solutions of the Hamilton--Jacobi equation

We find the form of the potential depending on the coordinates and the time such that a solution, $S$, of the Hamilton--Jacobi equation yields an exact solution, $\exp ({\rm i} S/\hbar)$, of the corresponding Schrödinger equation.

运动图像与量子力学中的Hamilton-Jacobi理论

Moving Picture and Hamilton-Jacobi Theory in Quantum Mechanics

本文提出了一种新的量子力学图像，我们称之为{ \it运动图像}。推导了这幅图中的薛定谔方程，并检验了它的解。我们还研究了运动图像与经典力学中的Hamilton-Jacobi理论之间的密切关系。

关于量子哈密顿-雅可比方程中李-哈密顿系统的一些特征

On some signatures of Lie-Hamilton System in Quantum Hamilton Jacobi Equation

本文研究了量子哈密顿-雅可比方程中李-哈密顿系统的特征，发现其可转换为凯利-克莱因里卡蒂方程，并探讨了李对称性和李积分。

广义PT对称Sinh-Gordon势在量子Hamilton-Jacobi形式下的可解性

The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism

在PT对称性的框架下，用量子哈密顿Jacobi方法求解了广义Sinh-Gordon势。得到了n= 0，1态广义Sinh-Gordon势的能量本征值和本征函数的准精确解.

量子哈密顿-雅可比量子化与形状不变性

Quantum Hamilton-Jacobi Quantization and Shape Invariance

本文证明常规势的可加形状不变性与未破缺超对称性足以保证其在量子哈密顿-雅可比量子化框架中可解，从而扩展了该方法的适用范围。

The quantum Hamilton Jacobi equation and the link between classical and quantum mechanics

We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the classical ones, this is not the case in the allowed regions. There, the limit is reached only if the quantum fluctuations are eliminated by means of coarse-graining averages. Analogously, the classical Hamilton-Jacobi scheme bringing to the motion's equations arises from a similar formal quantum procedure.

Novel formulation of Hamilton-Jacobi equation for higher derivative theory and quantum mechanical correspondence

For higher derivative theories, using the approach of Caratheodory's equivalent Lagrangian, we show that there exist novel formulations of Hamilton-Jacobi equations, which are different from the formulations derived from Hamilton's canonical approach. The quantum mechanical correspondences of these novel Hamilton-Jacobi equations lead to nonlinear quantum mechanics, which seem being able to avoid the unbounded negative energy problem in the quantum mechanics of higher derivative theories.

量子有效质量的Hamilton-Jacobi问题

The Quantum Effective Mass Hamilton-Jacobi Problem

本文研究了基于位置相关质量模型的量子哈密顿-雅可比理论.用两种具有不同奇异结构的有效质量函数来研究Morse势和Poschl-Teller势.利用留数法求出了量子有效质量- Hamilton Jacobi方程的解.进一步证明了Morse势和Poschl-Teller势的广义非厄米Swanson哈密顿量的本征态可以由Riccati方程得到，而不需要求解微分方程.