hamiltonian function

简明释义

哈密顿函数

英英释义

例句

1.The hamiltonian function 哈密顿函数 helps in transitioning from Lagrangian to Hamiltonian mechanics.

在从拉格朗日力学转向哈密顿力学时，哈密顿函数 hamiltonian function 具有重要作用。

2.The hamiltonian function 哈密顿函数 is crucial in formulating the equations of motion for a dynamical system.

在为动力系统制定运动方程时，哈密顿函数 hamiltonian function 是至关重要的。

3.By applying the hamiltonian function 哈密顿函数, physicists can simplify complex mechanical systems.

通过应用哈密顿函数 hamiltonian function，物理学家可以简化复杂的机械系统。

4.In quantum mechanics, the hamiltonian function 哈密顿函数 is represented as an operator that describes the energy of the system.

在量子力学中，哈密顿函数 hamiltonian function 被表示为描述系统能量的算符。

5.In classical mechanics, the hamiltonian function 哈密顿函数 represents the total energy of a system.

在经典力学中，哈密顿函数 hamiltonian function 表示一个系统的总能量。

作文

In the realm of physics and mathematics, the concept of the hamiltonian function plays a crucial role in understanding the dynamics of systems. Named after the Irish mathematician William Rowan Hamilton, this function provides a powerful framework for analyzing the behavior of physical systems over time. The hamiltonian function is particularly significant in classical mechanics, where it serves as a cornerstone for formulating equations of motion. Unlike the Lagrangian approach, which focuses on kinetic and potential energy, the hamiltonian function emphasizes the total energy of the system, allowing for a more comprehensive analysis of its dynamics.At its core, the hamiltonian function is defined as a function of generalized coordinates and momenta, representing the total energy of the system. Mathematically, it can be expressed as H(q, p) = T(q, p) + V(q), where H is the hamiltonian function, T is the kinetic energy, V is the potential energy, q represents the generalized coordinates, and p represents the generalized momenta. This formulation not only simplifies complex physical problems but also reveals deep insights into the conservation laws governing the system.One of the most striking features of the hamiltonian function is its ability to transition seamlessly between classical and quantum mechanics. In quantum mechanics, the hamiltonian function becomes an operator that governs the evolution of quantum states. This duality highlights the versatility of the hamiltonian function across different domains of physics, making it an indispensable tool for physicists and mathematicians alike.Moreover, the hamiltonian function is not limited to simple mechanical systems. It can be applied to a wide range of fields, including thermodynamics, electromagnetism, and even fields like economics and biology, where dynamic systems are analyzed. In each of these contexts, the hamiltonian function provides a structured way to examine the interplay between various variables and their impact on the overall system behavior.The significance of the hamiltonian function extends beyond theoretical applications; it has practical implications as well. Engineers and scientists utilize this framework to design systems that require precise control over dynamic behavior. For instance, in robotics, understanding the hamiltonian function allows for better control algorithms that ensure stability and efficiency in robotic movements.In conclusion, the hamiltonian function is a fundamental concept that bridges various disciplines within science and engineering. Its ability to encapsulate the total energy of a system and facilitate the analysis of its dynamics makes it an essential tool for understanding both classical and modern physics. As research continues to evolve, the hamiltonian function will undoubtedly remain a pivotal element in the exploration of complex systems, paving the way for new discoveries and innovations in numerous fields. Understanding the hamiltonian function is not just an academic exercise; it is a gateway to unlocking the mysteries of the universe and harnessing the principles of physics for practical applications.

在物理和数学领域，hamiltonian function的概念在理解系统动态方面发挥着至关重要的作用。这个函数以爱尔兰数学家威廉·罗恩·哈密顿的名字命名，为分析物理系统随时间变化的行为提供了强大的框架。hamiltonian function在经典力学中特别重要，它作为建立运动方程的基石。与侧重于动能和势能的拉格朗日方法不同，hamiltonian function强调系统的总能量，从而允许对其动态进行更全面的分析。从本质上讲，hamiltonian function被定义为广义坐标和动量的函数，表示系统的总能量。在数学上，它可以表示为 H(q, p) = T(q, p) + V(q)，其中 H 是 hamiltonian function，T 是动能，V 是势能，q 代表广义坐标，p 代表广义动量。这种表述不仅简化了复杂的物理问题，还揭示了支配系统的守恒定律的深刻见解。hamiltonian function最引人注目的特征之一是它能够在经典力学和量子力学之间无缝转换。在量子力学中，hamiltonian function变成一个操作符，控制量子态的演化。这种二元性突显了hamiltonian function在物理学不同领域中的多样性，使其成为物理学家和数学家不可或缺的工具。此外，hamiltonian function并不局限于简单的机械系统。它可以应用于广泛的领域，包括热力学、电磁学，甚至经济学和生物学等领域，在这些领域中分析动态系统。在每一个上下文中，hamiltonian function提供了一种结构化的方法来检查各种变量之间的相互作用及其对整体系统行为的影响。hamiltonian function的重要性不仅限于理论应用；它也具有实际意义。工程师和科学家利用这一框架设计需要精确控制动态行为的系统。例如，在机器人技术中，理解hamiltonian function可以更好地控制算法，确保机器人运动的稳定性和效率。总之，hamiltonian function是一个基本概念，连接了科学和工程各个学科。它能够概括系统的总能量，并促进对其动态的分析，使其成为理解经典和现代物理的基本工具。随着研究的不断发展，hamiltonian function无疑将继续成为探索复杂系统的关键元素，为多个领域的新发现和创新铺平道路。理解hamiltonian function不仅仅是一项学术练习；它是解锁宇宙奥秘和利用物理原理进行实际应用的门户。