Finite Element and Boundary Element Applications in Quantum Mechanics
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- 서양도서 > 과학/기술 > 수학 > 일반
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작가정보
저자(글) Ram-Mohan, L. Ramdas
목차
Introduction to the FEM Introduction p. 3 Basic concepts of quantum mechanics p. 4 Schrodinger's equation p. 4 Postulates of quantum mechanics p. 8 Principle of stationary action p. 10 The action integral p. 11 Examples p. 15 Finite elements p. 18 Historical comments p. 22 Problems p. 23 References p. 28 Simple quantum systems p. 31 The simple harmonic oscillator p. 31 The hydrogen atom p. 39 The Rayleigh-Ritz variational method p. 45 Programming considerations p. 50 Problems p. 57 References p. 60 Interpolation polynomials in one dimension p. 63 Introduction p. 63 Lagrange interpolation polynomials p. 64 Hermite interpolation polynomials p. 66 Transition elements p. 70 Low order interpolation polynomials p. 71 Low order Lagrange interpolation p. 71 Low order Hermite interpolation p. 72 Interpolation polynomials in Mathematica p. 72 Lagrange interpolation p. 72 Hermite interpolation p. 74 Infinite elements p. 76 Simple quantum systems revisited p. 77 Problems p. 80 References p. 81 Adaptive FEM p. 83 Introduction p. 83 Error in interpolation p. 84 Error in the discretized action p. 86 h-convergence p. 86 p-convergence p. 88 The action in adaptive calculations p. 91 An ordinary differential equation p. 92 The H atom again p. 96 Adaptive p-refinement p. 102 Concluding remarks p. 104 References p. 105 Applications in 1D Quantum mechanical tunneling p. 109 Introduction p. 109 Mixed BCs: redefining the action p. 110 The Galerkin method p. 113 Tunneling calculations in the FEM p. 115 Evaluation of the residual p. 115 Applying mixed BCs p. 118 Comparing Galerkin FEM with WKB p. 123 Quantum states in asymmetric wells p. 125 Problems p. 137 References p. 141 Schrodinger-Poisson self-consistency p. 145 Introduction p. 145 Schrodinger and Poisson equations p. 149 Source terms p. 151 The Fermi energy and charge neutrality p. 153 The Galerkin finite element approach p. 155 Boundary conditions p. 155 The iteration procedure p. 159 Numerical issues p. 161 Essential and natural boundary conditions p. 164 Further developments p. 165 Problems p. 167 References p. 169 Landau states in a magnetic field p. 171 Introduction p. 171 Landau levels p. 171 Density of states p. 174 Heterostructures in a B-field p. 177 Faraday configuration p. 177 Voigt configuration p. 179 Comparison with experiments p. 181 Interband transitions p. 181 Energy dependence on the orbit center p. 183 Level mixing in superlattices with small band offsets p. 185 Density of states in the Voigt geometry p. 186 Voigt geometry and a semiclassical model p. 188 Landau orbit theory p. 188 Envelope functions and the FEM in k-space p. 191 Problems p. 192 References p. 194 Wavefunction engineering p. 195 Introduction p. 195 k P theory of band structure p. 197 Designing mid-infrared lasers p. 200 The type-II W-laser p. 200 The interband cascade laser p. 206 Concluding comments p. 210 References p. 211 2D Applications of the FEM 2D elements and shape functions p. 217 Introduction p. 217 Rectangular elements p. 218 Lagrange elements p. 218 Hermite elements p. 221 Triangular elements p. 222 Defining curved edges p. 228 An element on a parametric curve p. 228 Parametric form of 2D surfaces p. 231 The action in 2D problems p. 233 Gauss integration in two dimensions p. 236 References p. 238 Mesh generation p. 241 Meshing simple regions p. 241 Distortion of regular regions p. 242 Using orthogonal curved coordinates p. 247 Regions of arbitrary shape p. 247 Delaunay meshing p. 247 Advancing front algorithms p. 248 The algebraic integer method p. 250 References p. 256 Applications in atomic physics p. 257 The H atom in a magnetic field p. 257 Schrodinger's equation and the action p. 258 Applying the FEM p. 259 Magnetic fields p. 266 Ground state energy in helium p. 269 Other results p. 271 References p. 273 Quantum wires p. 275 Introduction p. 275 Quantum wires and the FEM p. 276 Symmetry properties of the square wire p. 282 The checkerboard superlattice p. 285 Optical nonlinearity in the CBSL p. 289 Quantum wires of any cross-section p. 292 References p. 295 Quantum waveguides p. 299 Quantization of resistance p. 300 The straight waveguide p. 303 Quantum bound states in waveguides p. 311 The quantum interference transistor p. 313 "Stealth" elements and absorbing BC p. 315 The Ginzburg-Landau equation p. 322 References p. 323 Time-dependent problems p. 327 Introduction p. 327 Standard approaches to time evolution p. 327 Schrodinger's equation and the method of finite differences p. 327 The finite difference method for the wave equation p. 330 A transfer matrix for time evolution p. 331 Lanczos reduction of transfer matrices p. 335 Instability with initial conditions p. 338 Comparing IVBC and two-point BCs p. 338 The variational approach p. 347 A variational difficulty p. 347 Variations using adjoint functions p. 348 Adjoint variations for the wave equation p. 350 Connection with quantum field theory p. 352 Concluding remarks p. 355 References p. 356 Sparse Matrix Applications Matrix solvers and related issues p. 363 Introduction p. 363 Bandwidth reduction p. 363 Solution of linear equations p. 366 Gauss elimination p. 366 The conjugate gradient method p. 367 The standard eigenvalue problem p. 372 The generalized eigenvalue problem p. 373 Sturm sequence check p. 376 Inverse vector iteration p. 378 The subspace vectors p. 380 The Rayleigh quotient p. 381 Subspace iteration p. 383 The Davidson algorithm p. 385 Least square residual minimization p. 388 The Lanczos method p. 388 References p. 393 Boundary Elements The boundary element method p. 399 Introduction p. 399 The boundary integral p. 400 An analytical approach p. 402 A Dirichlet problem p. 402 A Neumann problem p. 406 Infinite domain Green's function p. 408 Numerical issues p. 414 Evaluation of the element integrals p. 414 Applying boundary conditions p. 415 Boundary condition at the corner node p. 417 Setting up the matrix equation p. 420 Construction of interior solution p. 422 A worked example p. 423 Two sum rules p. 425 Comparing the BEM with the FEM p. 427 Problems p. 428 References p. 432 The BEM and surface plasmons p. 435 Introduction p. 435 Multiregion BEM: two regions p. 437 Linear interpolation p. 437 Hermite interpolation p. 439 Bulk and surface plasmons p. 440 Bulk plasma oscillations p. 441 Surface plasmons at a single planar interface p. 443 Surface plasmons for slab geometry p. 447 Surface plasmons in a cylindrical wire p. 451 Two metallic wires p. 455 Metal wire on a substrate p. 458 Plasmons in other confining geometries p. 460 Surface-enhanced Raman scattering p. 461 Problems p. 462 References p. 468 The BEM and quantum applications p. 471 Introduction p. 471 2D electron waveguides p. 471 Implementing boundary conditions p. 477 Multiregion waveguide problems p. 483 Multiple ports and transmission p. 484 The BEM and 2D scattering p. 487 Eigenvalue problems and the BEM p. 491 Quantum wires p. 491 Hearing the shape of a drum p. 495 Concluding remarks on the BEM p. 498 Problems p. 501 References p. 505 Appendices Gauss quadrature p. 511 Introduction p. 511 Gauss-Legendre quadrature p. 511 Gauss-Legendre base points and weights p. 513 An algorithm for adaptive quadrature p. 517 Other Gauss formulas p. 519 The Cauchy principal value of an integral p. 520 Properties of Legendre functions p. 522 Problems p. 524 References p. 525 Generalized functions p. 527 The Dirac [delta]-function p. 527 The [delta]-function as the limit of a "normal" function p. 530 [delta]-functions in three dimensions p. 532 Other generalized functions p. 533 The step-function [theta](x) p. 533 The sign-function [varepsilon](x) p. 534 The Plemelj formula p. 535 An integral representation for [theta](z) p. 536 Problems p. 536 References p. 538 Green's functions p. 541 Introduction p. 541 Properties of Green's functions p. 543 Sturm-Liouville differential operators p. 547 Green's functions in electrostatics p. 554 Boundary integral solutions: a comment p. 557 Green's functions in electrodynamics p. 565 The wave equation in one dimension p. 570 The wave equation in two dimensions p. 573 Green's functions and integral equations p. 574 Problems p. 576 References p. 579 Physical constants p. 581 Author index p. 583 Subject index p. 597 Table of Contents provided by Syndetics. All Rights Reserved.
기본정보
ISBN | 9780198525226 ( 0198525222 ) |
---|---|
발행(출시)일자 | 2002년 11월 07일 |
쪽수 | 605쪽 |
크기 |
161 * 232
* 33
mm
/ 848 g
|
총권수 | 1권 |
언어 | 영어 |
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