04451nam a22006255i 4500 978-3-031-60065-4 DE-He213 20251030112923.0 cr nn 008mamaa 240831s2024 sz | s |||| 0|eng d 9783031600654 978-3-031-60065-4 10.1007/978-3-031-60065-4 doi QC173.45-173.458 PHFC bicssc SCI077000 bisacsh PHFC thema Iurov, Andrii. author. aut http://id.loc.gov/vocabulary/relators/aut 83288 A Tutorial on the WKB Approximation for Innovative Dirac Materials [electronic resource] : Graphene and Beyond / by Andrii Iurov. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 383 p. 78 illus., 77 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Tracts in Modern Physics, 1615-0430 ; 292 Chapter 1 Introduction and Overview (1) -- Chapter 2 Introduction and Overview (2) -- Chapter 3 Basic Formulation of the Wentzel–Kramers–Brillouin (WKB) Theory -- Chapter 4 Describing Actual Quantum Systems Using the WKB Theory -- Chapter 5 Dirac Cone Materials -- Chapter 6 Semiclassical Approximation for Graphene -- Chapter 7 WKB Theory for 𝜶 − T3 Materials and a Dice Lattice -- Chapter 8 Applications of WKB Equations for Dirac Materials -- Chapter 9 Concluding Remarks and Research Outlook. This textbook serves to supplement existing quantum mechanics courses with the WKB (Wentzel–Kramers–Brillouin) theory for recently discovered Dirac materials, such as graphene, a dice lattice, and alpha-T3 materials. This includes finding the semiclassical wave function, coordinate-dependent momentum, semiclassical action, the complete set of transport equations, and applicability conditions for the approximation. The discovery of graphene and its unique electronic behavior has transformed research in condensed matter physics over the last 10-15 years, but core curriculum in standard graduate-level physics courses still does not reflect these new developments and this book intends to close this gap. With a clear focus on various types of Dirac Hamiltonians, the multidimensional theory is only a small part of the book. The derivation of the WKB equations for novel Dirac materials and their applications to electron tunneling, turning points and classically forbidden regions, resonances and localized states, and many other crucial physical problems are methodically presented. This textbook aims to expand the existing approach to presenting the WKB approximation and covers recent developments in its applications. This book also includes many informative graphics, as well as problems and exercises with hints at the end of each chapter. Additional detailed mathematical derivations, as well as code in Mathematica, are added throughout the whole book. Ideal for graduate students and researchers in condensed matter physics, this textbook serves as a modern guide for learning the WKB theory. Condensed matter. 66773 Materials science Data processing. 67985 Electronic structure. 83289 Quantum chemistry Computer programs. 83290 Photonic crystals. 83291 Quantum optics. Mathematical physics. Two-dimensional Materials. 71610 Electronic Structure Calculations. 83292 Photonic Crystals. 83293 Quantum Optics. Mathematical Methods in Physics. 70877 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031600647 Printed edition: 9783031600661 Printed edition: 9783031600678 Springer Tracts in Modern Physics, 1615-0430 ; 292 71873 https://doi.org/10.1007/978-3-031-60065-4 ZDB-2-PHA ZDB-2-SXP 62908 62908