LEADER 04436nam 22007215 450 001 9910886087803321 005 20240831130306.0 010 $a3-031-60065-7 024 7 $a10.1007/978-3-031-60065-4 035 $a(CKB)34605115700041 035 $a(MiAaPQ)EBC31629251 035 $a(Au-PeEL)EBL31629251 035 $a(DE-He213)978-3-031-60065-4 035 $a(EXLCZ)9934605115700041 100 $a20240831d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Tutorial on the WKB Approximation for Innovative Dirac Materials $eGraphene and Beyond /$fby Andrii Iurov 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (389 pages) 225 1 $aSpringer Tracts in Modern Physics,$x1615-0430 ;$v292 311 $a3-031-60064-9 327 $aChapter 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 ? ? T3 Materials and a Dice Lattice -- Chapter 8 Applications of WKB Equations for Dirac Materials -- Chapter 9 Concluding Remarks and Research Outlook. 330 $aThis textbook serves to supplement existing quantum mechanics courses with the WKB (Wentzel?Kramers?Brillouin) theory for recently discovered Dirac materials, such as graphene, a dice lattice, and alpha-T3 materials. This includes finding the semiclassical wave function, coordinate-dependent momentum, semiclassical action, the complete set of transport equations, and applicability conditions for the approximation. The discovery of graphene and its unique electronic behavior has transformed research in condensed matter physics over the last 10-15 years, but core curriculum in standard graduate-level physics courses still does not reflect these new developments and this book intends to close this gap. With a clear focus on various types of Dirac Hamiltonians, the multidimensional theory is only a small part of the book. The derivation of the WKB equations for novel Dirac materials and their applications to electron tunneling, turning points and classically forbidden regions, resonances and localized states, and many other crucial physical problems are methodically presented. This textbook aims to expand the existing approach to presenting the WKB approximation and covers recent developments in its applications. This book also includes many informative graphics, as well as problems and exercises with hints at the end of each chapter. Additional detailed mathematical derivations, as well as code in Mathematica, are added throughout the whole book. Ideal for graduate students and researchers in condensed matter physics, this textbook serves as a modern guide for learning the WKB theory. 410 0$aSpringer Tracts in Modern Physics,$x1615-0430 ;$v292 606 $aCondensed matter 606 $aMaterials science$xData processing 606 $aElectronic structure 606 $aQuantum chemistry$xComputer programs 606 $aPhotonic crystals 606 $aQuantum optics 606 $aMathematical physics 606 $aTwo-dimensional Materials 606 $aElectronic Structure Calculations 606 $aPhotonic Crystals 606 $aQuantum Optics 606 $aMathematical Methods in Physics 615 0$aCondensed matter. 615 0$aMaterials science$xData processing. 615 0$aElectronic structure. 615 0$aQuantum chemistry$xComputer programs. 615 0$aPhotonic crystals. 615 0$aQuantum optics. 615 0$aMathematical physics. 615 14$aTwo-dimensional Materials. 615 24$aElectronic Structure Calculations. 615 24$aPhotonic Crystals. 615 24$aQuantum Optics. 615 24$aMathematical Methods in Physics. 676 $a530.41 676 $a620.19 700 $aIurov$b Andrii$01770624 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910886087803321 996 $aA Tutorial on the WKB Approximation for Innovative Dirac Materials$94252827 997 $aUNINA