one electron approximation

简明释义

单电子近似

英英释义

例句

1.Although the one electron approximation 单电子近似 simplifies many problems, it may not be valid for multi-electron systems.

虽然单电子近似 one electron approximation 简化了许多问题，但它可能不适用于多电子系统。

2.The one electron approximation 单电子近似 is often used in the Hartree-Fock method to estimate the energy levels of electrons.

在哈特里-福克方法中，通常使用单电子近似 one electron approximation 来估算电子的能级。

3.In quantum chemistry, the one electron approximation 单电子近似 simplifies the calculations by assuming that each electron moves independently in the field of the nucleus.

在量子化学中，单电子近似 one electron approximation 通过假设每个电子在核的场中独立运动来简化计算。

4.In solid-state physics, the one electron approximation 单电子近似 helps in understanding the behavior of conduction electrons in metals.

在固态物理中，单电子近似 one electron approximation 有助于理解金属中导电电子的行为。

5.When studying hydrogen-like atoms, the one electron approximation 单电子近似 provides a good first-order solution.

在研究氢样原子时，单电子近似 one electron approximation 提供了一个良好的一级解。

作文

The concept of the one electron approximation plays a critical role in the field of quantum mechanics and atomic physics. This approximation simplifies the complex interactions between multiple electrons in an atom by considering only one electron at a time while treating the effects of all other electrons as a constant background potential. This approach is particularly useful when dealing with multi-electron atoms where the full many-body problem becomes mathematically intractable. By applying the one electron approximation, physicists can derive important properties of atoms without getting lost in the overwhelming complexity of electron-electron interactions.In essence, the one electron approximation allows researchers to focus on the behavior of individual electrons in an atom, which can then be analyzed using well-established quantum mechanical principles. For example, when studying the hydrogen atom, which consists of one proton and one electron, this approximation yields accurate results because there are no other electrons to consider. However, for more complex atoms, such as those found in the periodic table, this method provides a first-order understanding that can be refined with additional corrections.One of the significant implications of the one electron approximation is its application in the development of atomic models, such as the Bohr model. The Bohr model, which describes the quantized orbits of electrons around the nucleus, relies heavily on the simplification provided by this approximation. Although it does not account for the repulsion between multiple electrons, it offers a foundational understanding of atomic structure that can be built upon with more sophisticated theories.Moreover, the one electron approximation is not limited to atomic physics; it finds applications in solid-state physics as well. In the study of semiconductors and metals, the behavior of conduction electrons can often be approximated as if they were independent particles moving in a periodic potential created by the lattice of ions. This perspective leads to the development of band theory, which is crucial for understanding electrical conductivity and the electronic properties of materials.However, it is essential to recognize the limitations of the one electron approximation. While it provides a useful starting point, it cannot fully capture the intricacies of electron correlation and exchange effects that occur in multi-electron systems. As a result, more advanced techniques, such as configuration interaction and density functional theory, have been developed to address these shortcomings. These methods incorporate the interactions between electrons more accurately, yet they often require significant computational resources.In conclusion, the one electron approximation serves as a vital tool in the arsenal of physicists and chemists, enabling them to simplify the complexities of atomic and molecular systems. By focusing on the behavior of individual electrons and treating the rest as a constant background, researchers can gain insights into atomic structure, chemical bonding, and material properties. Despite its limitations, the one electron approximation remains a cornerstone of theoretical approaches in quantum mechanics, paving the way for more comprehensive models and a deeper understanding of the fundamental principles governing matter.

“单电子近似”这一概念在量子力学和原子物理学领域中起着至关重要的作用。该近似通过考虑单个电子的行为，同时将其他所有电子的影响视为常数背景势，来简化原子中多个电子之间的复杂相互作用。这种方法在处理多电子原子时尤为有用，因为完整的多体问题在数学上变得难以处理。通过应用“单电子近似”，物理学家可以推导出原子的许多重要性质，而不会迷失在电子-电子相互作用的压倒性复杂性中。从本质上讲，“单电子近似”使研究人员能够专注于原子中单个电子的行为，这可以利用成熟的量子力学原理进行分析。例如，在研究氢原子时，由于氢原子由一个质子和一个电子组成，这种近似提供了准确的结果，因为没有其他电子需要考虑。然而，对于更复杂的原子，如周期表中的原子，该方法提供了一种一阶理解，可以通过附加修正进行完善。“单电子近似”的一个重要意义是它在原子模型发展中的应用，例如波尔模型。波尔模型描述了电子围绕原子核的量子化轨道，严重依赖于这一近似所提供的简化。尽管它没有考虑多个电子之间的排斥，但它提供了对原子结构的基础理解，可以在此基础上建立更复杂的理论。此外，“单电子近似”并不仅限于原子物理学；它在固态物理学中也有应用。在研究半导体和金属时，导电电子的行为常常可以近似为独立粒子，在离子晶格产生的周期性势场中运动。这种视角导致了带理论的发展，这是理解电导率和材料电子特性的关键。然而，必须认识到“单电子近似”的局限性。虽然它提供了一个有用的起点，但无法完全捕捉多电子系统中发生的电子关联和交换效应的复杂性。因此，已经开发出更先进的技术，如配置相互作用和密度泛函理论，以解决这些缺陷。这些方法更准确地结合了电子之间的相互作用，但通常需要大量的计算资源。总之，“单电子近似”作为物理学家和化学家的重要工具，使他们能够简化原子和分子系统的复杂性。通过专注于单个电子的行为，并将其余部分视为常数背景，研究人员可以深入了解原子结构、化学键合和材料性质。尽管存在局限性，但“单电子近似”仍然是量子力学理论方法的基石，为更全面的模型和对支配物质基本原理的更深入理解铺平了道路。