# Monte Carlo methods [electronic resource] : a hands-on computational introduction utilizing Excel / Sujaul Chowdhury

- Author:
- Chowdhury, Sujaul
- Published:
- San Rafael, California (1537 Fourth Street, 1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, [2021]
- Physical Description:
- 1 PDF (x, 123 pages) : illustrations (some color).

##### Access Online

- Series:
- Synthesis lectures on mathematics and statistics, 1938-1751 ; #37
- Restrictions on Access:
- License restrictions may limit access.
- Contents:
- 1. Introduction -- 1.1. Random variable -- 1.2. Continuous random variable -- 1.3. Uniform random variable -- 1.4. Normal or gaussian random variable -- 1.5. Transformation or modeling of random variable -- 1.6. Examples of transformation or modeling of random variable -- 1.7. Variance reduction and importance sampling, 2. Evaluation of definite integrals using the Monte Carlo method -- 2.1. Evaluation of definite integrals using the Monte Carlo method : example I -- 2.2. Evaluation of definite integrals using the Monte Carlo method : example II -- 2.3. Evaluation of definite integrals using the Monte Carlo method : example III -- 2.4. Evaluation of definite integrals using the Monte Carlo method : example IV -- 2.5. Evaluation of definite integrals using the Monte Carlo method : example V, 3. Variational Monte Carlo Method applied to the ground state of a simple harmonic oscillator -- 3.1. The variational method of quantum mechanics applied to the ground state of any quantum mechanical system -- 3.2. The variational method of quantum mechanics applied to the ground state of a simple harmonic oscillator -- 3.3. Ground state energy of a simple harmonic oscillator using the Monte Carlo method, and 4. Variational Monte Carlo method applied to the ground state of a hydrogen atom -- 4.1. The variational method of quantum mechanics applied to the ground state of any quantum mechanical system (again) -- 4.2. The variational method of quantum mechanics applied to the ground state of a hydrogen atom -- 4.3. Ground state energy of a hydrogen atom using the variational Monte Carlo method -- 5. Concluding remarks.
- Summary:
- 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 F(x), namely Sin(x), Cos(x), ex, loge(x), and 1/(1+x2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions p(x). It is shown that results agree with known exact values better if p(x) is proportional to F(x). 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 "Computational Physics." 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.
- Subject(s):
- Genre(s):
- ISBN:
- 9781636390727 electronic, 9781636390734 hardcover, and 9781636390710 paperback
- Note:
- Part of: Synthesis digital library of engineering and computer science.
- Bibliography Note:
- Includes bibliographical references (page 121).
- Technical Details:
- Mode of access: World Wide Web. and System requirements: Adobe Acrobat Reader.

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