标题： 流体力学薛定谔方程的改革和等熵无粘势流的拉格朗日场理论 显示英文标题

标题： The reform of hydrodynamic Schrödinger equation and Lagrangian field theory for barotropic inviscid potential flow

摘要： 本文提出了一种改进的框架，以解决现有流体力学薛定谔方程（HSE）框架中的关键问题。 通过解除对粒子质量的依赖并引入校正项以消除量子势，该框架与经典流体力学实现了更好的一致性。 我们定义了一个新的算子，称为“特定哈密顿算子”，这确保了可以从拉格朗日场论推导出改进的流体力学薛定谔方程（RHSE）。 对于等熵无粘势流的RHSE进行了开发并通过诺特定理进行了验证，证明该校正项施加了经典能量守恒。 尽管所得方程高度非线性，但这种方法为连接量子力学和经典流体力学提供了一条有效的途径。 显示英文摘要

摘要： This paper presents a reformed framework to address key issues in the existing hydrodynamic Schr\"odinger equation (HSE) framework. By disengaging the dependence on particle mass and introducing a correction term to eliminate quantum potential, the framework achieves better alignment with classical fluid mechanics. We define a new operator, designated as "specific Hamiltonian operator," which ensures that a reformed hydrodynamic Schr\"odinger equation (RHSE) is derivable from Lagrangian field theory. The RHSE for barotropic inviscid potential flow is developed and validated through Noether's theorem, demonstrating that the correction imposes the conservation of classical energy. While the resulting equations are highly nonlinear, this approach offers an effective pathway for bridging quantum mechanics and classical fluid mechanics.