Overview

Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that ""something else"" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this ""something else"", but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The piece de resistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schroedinger breather as a function of its width.

Full Product Details

Author:   Maxim Olchanyi (Olshanii) (Univ Of Massachusetts At Boston, Usa)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Dimensions:   Width: 15.20cm , Height: 1.80cm , Length: 22.90cm
Weight:   0.408kg
ISBN:  

9789814508469

ISBN 10:   9814508462
Pages:   172
Publication Date:   14 November 2013
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

WKB Approximation; Halved Harmonic Oscillator: A Case Study; Perturbation Theory; Variational Problems; Gravitational Well: A Case Study; Some Exotic Exactly Solvable Problems; Mean-Field Theories; Integrable Nonlinear Partial Differential Equations.

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