Statistical Complexity: Applications in Electronic Structure

The understanding of electron density as the carrier of all the information of a multielectronic system is implicit in the theorems of density functional theory. Information theoretical based measures giving a quantitative understanding of statistical complexity of such systems is shaping up as a new area of research in chemical physics. This book is the first monograph of its kind covering the aspects of complexity measure in atoms and molecules

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4.3.1 Fisher-Shannon Information: De?nition and Properties.

Statistical Complexity; Foreword; Preface; Contents; Contributors; Chapter 1: Entropic Uncertainty Relations in Quantum Physics; 1.1 Introduction; 1.2 Information Entropy as a Measure of Uncertainty; 1.2.1 Standard Deviation; 1.2.2 Limitations on the Use of Standard Deviations; 1.2.2.1 Example I; 1.2.2.2 Example II; 1.2.3 Uncertainty of Measurements; 1.2.4 Shannon Entropy; 1.2.4.1 Examples; 1.2.5 Entropic Uncertainty Relations; 1.3 Rényi Entropy; 1.3.1 Rényi Entropy and the Uncertainty Relations; 1.4 Uncertainty Relations: From Discrete to Continuous.

1.4.1 The Uncertainty Relations for N-level Systems1.4.1.1 Deutsch Inequality; 1.4.1.2 Maassen-Uf?nk Inequalities; 1.4.1.3 Discrete Fourier Transform; 1.4.2 Shannon and Rényi Entropies for Continuous Distributions; 1.4.3 Uncertainty Relations for Continuous Entropies; 1.4.3.1 Gaussian Wave Functions; 1.5 Generalizations and Extensions; 1.5.1 Uncertainty Relations for Mixed States; 1.5.2 Uncertainty Relations for Angles and Angular Momenta; 1.5.2.1 The Uncertainty Relation for a Particle on a Circle; 1.5.2.2 The Uncertainty Relation for a Particle on the Surface of a Sphere.

1.5.3 Uncertainty Relations in Phase Space1.5.4 Mutually U…