hamiltonian operator

简明释义

哈密顿算符

英英释义

例句

1.To solve the Schrödinger equation, one must first determine the appropriate hamiltonian operator for the system being studied.

为了求解薛定谔方程，首先必须确定所研究系统的合适的哈密顿算符。

2.When analyzing the dynamics of particles, physicists often refer to the hamiltonian operator to understand energy conservation.

在分析粒子的动力学时，物理学家常常引用哈密顿算符来理解能量守恒。

3.The time-dependent hamiltonian operator can change as external fields are applied to the system.

时间依赖的哈密顿算符可以随着外部场施加到系统上而变化。

4.The hamiltonian operator is crucial in determining the stationary states of a quantum system.

哈密顿算符在确定量子系统的驻态方面至关重要。

5.In quantum mechanics, the evolution of a system is governed by the hamiltonian operator, which represents the total energy of the system.

在量子力学中，系统的演化由哈密顿算符支配，它表示系统的总能量。

作文

The concept of the hamiltonian operator is fundamental in the field of quantum mechanics and classical mechanics. It serves as a cornerstone for understanding the dynamics of physical systems. In essence, the hamiltonian operator represents the total energy of a system, encapsulating both kinetic and potential energies. This operator is crucial for formulating the equations of motion that govern the behavior of particles and fields in physics.To delve deeper into the significance of the hamiltonian operator, it is important to first understand its mathematical formulation. In classical mechanics, the Hamiltonian is expressed as a function of generalized coordinates and momenta. This formulation leads to Hamilton's equations, which provide a powerful framework for analyzing dynamical systems. In quantum mechanics, the hamiltonian operator takes on an operator form, acting on the wave functions of quantum states. The time evolution of these states is governed by the Schrödinger equation, where the hamiltonian operator plays a pivotal role.One of the remarkable aspects of the hamiltonian operator is its ability to reveal symmetries and conservation laws in physical systems. According to Noether's theorem, every differentiable symmetry of the action of a physical system corresponds to a conservation law. For instance, if a system exhibits translational symmetry, the hamiltonian operator can be used to demonstrate the conservation of momentum. Similarly, rotational symmetry leads to the conservation of angular momentum. These connections highlight the profound relationship between symmetry and conservation in physics.Moreover, the hamiltonian operator facilitates the transition from classical to quantum mechanics. As physicists sought to describe the behavior of particles at the quantum level, the Hamiltonian formalism provided a natural bridge. By quantizing the classical Hamiltonian, researchers were able to derive the quantum mechanical description of systems, leading to groundbreaking discoveries in atomic and subatomic physics.In practical applications, the hamiltonian operator is employed in various fields, including condensed matter physics, quantum field theory, and even in the study of complex systems like biological molecules. In condensed matter physics, for example, the Hamiltonian describes the interactions between electrons in a solid, allowing scientists to understand phenomena such as superconductivity and magnetism. In quantum field theory, the hamiltonian operator is essential for describing particle interactions and the dynamics of fields.In conclusion, the hamiltonian operator is a powerful tool that underpins much of modern physics. Its role in defining the energy of a system, guiding the equations of motion, revealing symmetries, and facilitating the transition from classical to quantum mechanics cannot be overstated. As we continue to explore the complexities of the universe, the hamiltonian operator will undoubtedly remain a central figure in our quest for understanding the fundamental laws of nature.

“哈密顿算子”这个概念在量子力学和经典力学领域中是基础性的。它是理解物理系统动态的基石。从本质上讲，hamiltonian operator代表了一个系统的总能量，包括动能和势能。这个算子对于制定支配粒子和场行为的运动方程至关重要。为了更深入地理解hamiltonian operator的重要性，首先需要了解它的数学形式。在经典力学中，哈密顿量被表示为广义坐标和动量的函数。这种表述导致了哈密顿方程，为分析动态系统提供了强大的框架。在量子力学中，hamiltonian operator以算子的形式出现，作用于量子态的波函数。量子态的时间演化由薛定谔方程支配，其中hamiltonian operator扮演着关键角色。hamiltonian operator的一个显著特点是它能够揭示物理系统中的对称性和守恒定律。根据诺特定理，物理系统作用的每一个可微对称性对应于一个守恒定律。例如，如果一个系统表现出平移对称性，则可以使用hamiltonian operator来证明动量的守恒。同样，旋转对称性导致角动量的守恒。这些联系突显了物理学中对称性与守恒之间的深刻关系。此外，hamiltonian operator促进了从经典到量子力学的过渡。当物理学家试图描述量子水平上的粒子行为时，哈密顿形式主义提供了一个自然的桥梁。通过对经典哈密顿量进行量子化，研究人员能够推导出系统的量子力学描述，从而在原子和亚原子物理学中取得了突破性的发现。在实际应用中，hamiltonian operator被广泛应用于凝聚态物理、量子场论，甚至复杂系统如生物分子的研究中。例如，在凝聚态物理中，哈密顿量描述了固体中电子之间的相互作用，使科学家能够理解超导性和磁性等现象。在量子场论中，hamiltonian operator对于描述粒子相互作用和场的动态至关重要。总之，hamiltonian operator是现代物理学的一个强大工具。它在定义系统能量、指导运动方程、揭示对称性以及促进经典与量子力学之间的过渡中的作用不可低估。随着我们继续探索宇宙的复杂性，hamiltonian operator无疑将继续成为我们理解自然基本法则的中心人物。