Computational Physics: Simulation of Classical and Quantum Systems
计算物理：经典和量子系统的模拟

Author: Philipp O.J. Scherer

下载地址：https://www.zhisci.com/pdfshow/17740

This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. Many clear mathematical descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study the properties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space. Besides the classical methods, inverse interpolation is discussed, together with the popular combined methods by Dekker and Brent and a not so well known improvement by Chandrupatla. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. A comparison of several methods for quantum systems is performed, containing pseudo-spectral methods, finite differences methods, rational approximation to the time evolution operator, second order differencing and split operator methods.
这本教科书介绍了基础和先进的计算物理在一个非常说教的风格。它包含了计算物理中使用的许多最重要算法的非常好的呈现和简单的数学描述。对计算物理中的重要技术给出了许多清晰的数学描述。书的第一部分讨论了基本的数值方法。大量的练习和计算机实验允许研究这些方法的性质。第二部分集中于经典系统和量子系统的模拟。它对运动方程使用了一个相当普遍的概念，可以应用于常微分方程和偏微分方程。讨论了几种积分方法，不仅包括标准Euler和Runge-Kutta方法，还包括多步方法和通过研究Liouville空间中的运动引入的Verlet方法。除了经典方法外，还讨论了逆插值，以及Dekker和Brent的常用组合方法以及Chandrupatla的一个不为人所知的改进。关于微分方程数值处理的一般章节提供了有限差分法、有限体积法、有限元法和边界元法以及基于谱法和加权残差法的方法。比较了量子系统的几种方法，包括伪谱方法、有限差分方法、时间演化算子的有理逼近、二阶微分和分裂算子方法。

The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into the numerical treatment but also the simulated problems. Rotational motion is treated in much detail to describe the motion of rigid rotors which can be just a simple spinning top or a collection of molecules or planets. The behaviour of simple quantum systems is studied thoroughly. One focus is on a two level system in an external field. Solution of the Bloch equations allows the simulation of a quantum bit and to understand elementary principles from quantum optics. As an example of a thermodynamic system, the Lennard Jones liquid is simulated. The principles of molecular dynamics are shown with practical simulations. A second thermodynamic topic is the Ising model in one and two dimensions. The solution of the Poisson Boltzman equation is discussed in detail which is very important in Biophysics as well as in semiconductor physics. Besides the standard finite element methods, also modern boundary element methods are discussed. Waves and diffusion processes are simulated. Different methods are compared with regard to their stability and efficiency. Random walk models are studied with application to basic polymer physics. Nonlinear systems are discussed in detail with application to population dynamics and reaction diffusion systems. The exercises to the book are realized as computer experiments. A large number of Java applets is provided. It can be tried out by the reader even without programming skills. The interested reader can modify the programs with the help of the freely available and platform independent programming environment "netbeans".
这本书给出了简单但不平凡的例子，从一个广泛的物理主题试图给读者洞察数字处理，也模拟问题。旋转运动被详细地处理来描述刚性转子的运动，这些转子可以是简单的旋转陀螺，也可以是分子或行星的集合。对简单量子系统的行为进行了深入的研究。其中一个重点是外部领域的两级系统。布洛赫方程组的求解可以模拟量子比特，并从量子光学中理解基本原理。作为一个热力学系统的例子，对Lennard-Jones液体进行了模拟。通过实际模拟，说明了分子动力学原理。第二个热力学主题是一维和二维的伊辛模型。详细讨论了泊松-玻尔兹曼方程的求解方法，该方程在生物物理和半导体物理中都是非常重要的。除了标准的有限元方法外，还讨论了现代边界元方法。模拟了波浪和扩散过程。比较了不同方法的稳定性和效率。研究了随机游走模型及其在聚合物基础物理中的应用。详细讨论了非线性系统在人口动力学和反应扩散系统中的应用。这本书的练习是作为计算机实验来实现的。提供了大量的Java小程序。即使没有编程技巧，读者也可以试用它。感兴趣的读者可以在免费的、独立于平台的编程环境netbeans的帮助下修改程序。

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