Bøger af Sujaul Chowdhury

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.

This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method.

This book discusses topics related to Newtonian mechanics and is ideal for a one semester course. Introductory topics are first presented including: time, space, and matter; different coordinate systems; vectors; and unit vectors;. The author presents tools such as displacement, velocity, and acceleration to describe projectile motion and uniform circular motion. Newton's laws of motion and concepts of force and mass are discussed followed by kinetic energy, potential energy, and both conservative and non-conservative forces. This class-tested book also introduces angular displacement, angular speed, and angular acceleration as well as the use of these to describe the motion of particles with constant angular acceleration. Concepts of torque, angular momentum, and rotational inertia are presented to explain the motion of physical pendulum. Motion under central force is also covered and Kepler's laws are derived.

This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.

This book is intended for undergraduate students of Mathematics, Statistics, and Physics who know nothing about Monte Carlo Methods but wish to know how they work. All treatments have been done as much manually as is practicable. The treatments are deliberately manual to let the readers get the real feel of how Monte Carlo Methods work. Definite integrals of a total of five functions ,,,,(,,,,), namely Sin(,,,,), Cos(,,,,), e,,,,, loge(,,,,), and 1/(1+,,,,2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions ,,,,(,,,,). It is shown that results agree with known exact values better if ,,,,(,,,,) is proportional to ,,,,(,,,,). Deviation from the proportionality results in worse agreement. This book is on Monte Carlo Methods which are numerical methods for Computational Physics. These are parts of a syllabus for undergraduate students of Mathematics and Physics for the course titled "e;Computational Physics."e;Need for the book: Besides the three referenced books, this is the only book that teaches how basic Monte Carlo methods work. This book is much more explicit and easier to follow than the three referenced books. The two chapters on the Variational Quantum Monte Carlo method are additional contributions of the book. Pedagogical features: After a thorough acquaintance with background knowledge in Chapter 1, five thoroughly worked out examples on how to carry out Monte Carlo integration is included in Chapter 2. Moreover, the book contains two chapters on the Variational Quantum Monte Carlo method applied to a simple harmonic oscillator and a hydrogen atom. The book is a good read; it is intended to make readers adept at using the method. The book is intended to aid in hands-on learning of the Monte Carlo methods.

Contains an extensive illustration of use of the finite difference method in solving the boundary value problem numerically. A wide class of differential equations are numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, the book solves special functions such as Hermite.

Contains an account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force, motion under Hooke's law force, and motion under a combination of Hooke's law force and a velocity dependent damping force.