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Finite Element and Boundary Element Applications in Quantum Mechanics

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2013년 9월 9일 이후 누적수치입니다.

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Finite Element and Boundary Element Applications in Quantum Mechanics

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Introduction to the FEM
Introductionp. 3
Basic concepts of quantum mechanicsp. 4
Schrodinger's equationp. 4
Postulates of quantum mechanicsp. 8
Principle of stationary actionp. 10
The action integralp. 11
Examplesp. 15
Finite elementsp. 18
Historical commentsp. 22
Problemsp. 23
Referencesp. 28
Simple quantum systemsp. 31
The simple harmonic oscillatorp. 31
The hydrogen atomp. 39
The Rayleigh-Ritz variational methodp. 45
Programming considerationsp. 50
Problemsp. 57
Referencesp. 60
Interpolation polynomials in one dimensionp. 63
Introductionp. 63
Lagrange interpolation polynomialsp. 64
Hermite interpolation polynomialsp. 66
Transition elementsp. 70
Low order interpolation polynomialsp. 71
Low order Lagrange interpolationp. 71
Low order Hermite interpolationp. 72
Interpolation polynomials in Mathematicap. 72
Lagrange interpolationp. 72
Hermite interpolationp. 74
Infinite elementsp. 76
Simple quantum systems revisitedp. 77
Problemsp. 80
Referencesp. 81
Adaptive FEMp. 83
Introductionp. 83
Error in interpolationp. 84
Error in the discretized actionp. 86
h-convergencep. 86
p-convergencep. 88
The action in adaptive calculationsp. 91
An ordinary differential equationp. 92
The H atom againp. 96
Adaptive p-refinementp. 102
Concluding remarksp. 104
Referencesp. 105
Applications in 1D
Quantum mechanical tunnelingp. 109
Introductionp. 109
Mixed BCs: redefining the actionp. 110
The Galerkin methodp. 113
Tunneling calculations in the FEMp. 115
Evaluation of the residualp. 115
Applying mixed BCsp. 118
Comparing Galerkin FEM with WKBp. 123
Quantum states in asymmetric wellsp. 125
Problemsp. 137
Referencesp. 141
Schrodinger-Poisson self-consistencyp. 145
Introductionp. 145
Schrodinger and Poisson equationsp. 149
Source termsp. 151
The Fermi energy and charge neutralityp. 153
The Galerkin finite element approachp. 155
Boundary conditionsp. 155
The iteration procedurep. 159
Numerical issuesp. 161
Essential and natural boundary conditionsp. 164
Further developmentsp. 165
Problemsp. 167
Referencesp. 169
Landau states in a magnetic fieldp. 171
Introductionp. 171
Landau levelsp. 171
Density of statesp. 174
Heterostructures in a B-fieldp. 177
Faraday configurationp. 177
Voigt configurationp. 179
Comparison with experimentsp. 181
Interband transitionsp. 181
Energy dependence on the orbit centerp. 183
Level mixing in superlattices with small band offsetsp. 185
Density of states in the Voigt geometryp. 186
Voigt geometry and a semiclassical modelp. 188
Landau orbit theoryp. 188
Envelope functions and the FEM in k-spacep. 191
Problemsp. 192
Referencesp. 194
Wavefunction engineeringp. 195
Introductionp. 195
k P theory of band structurep. 197
Designing mid-infrared lasersp. 200
The type-II W-laserp. 200
The interband cascade laserp. 206
Concluding commentsp. 210
Referencesp. 211
2D Applications of the FEM
2D elements and shape functionsp. 217
Introductionp. 217
Rectangular elementsp. 218
Lagrange elementsp. 218
Hermite elementsp. 221
Triangular elementsp. 222
Defining curved edgesp. 228
An element on a parametric curvep. 228
Parametric form of 2D surfacesp. 231
The action in 2D problemsp. 233
Gauss integration in two dimensionsp. 236
Referencesp. 238
Mesh generationp. 241
Meshing simple regionsp. 241
Distortion of regular regionsp. 242
Using orthogonal curved coordinatesp. 247
Regions of arbitrary shapep. 247
Delaunay meshingp. 247
Advancing front algorithmsp. 248
The algebraic integer methodp. 250
Referencesp. 256
Applications in atomic physicsp. 257
The H atom in a magnetic fieldp. 257
Schrodinger's equation and the actionp. 258
Applying the FEMp. 259
Magnetic fieldsp. 266
Ground state energy in heliump. 269
Other resultsp. 271
Referencesp. 273
Quantum wiresp. 275
Introductionp. 275
Quantum wires and the FEMp. 276
Symmetry properties of the square wirep. 282
The checkerboard superlatticep. 285
Optical nonlinearity in the CBSLp. 289
Quantum wires of any cross-sectionp. 292
Referencesp. 295
Quantum waveguidesp. 299
Quantization of resistancep. 300
The straight waveguidep. 303
Quantum bound states in waveguidesp. 311
The quantum interference transistorp. 313
"Stealth" elements and absorbing BCp. 315
The Ginzburg-Landau equationp. 322
Referencesp. 323
Time-dependent problemsp. 327
Introductionp. 327
Standard approaches to time evolutionp. 327
Schrodinger's equation and the method of finite differencesp. 327
The finite difference method for the wave equationp. 330
A transfer matrix for time evolutionp. 331
Lanczos reduction of transfer matricesp. 335
Instability with initial conditionsp. 338
Comparing IVBC and two-point BCsp. 338
The variational approachp. 347
A variational difficultyp. 347
Variations using adjoint functionsp. 348
Adjoint variations for the wave equationp. 350
Connection with quantum field theoryp. 352
Concluding remarksp. 355
Referencesp. 356
Sparse Matrix Applications
Matrix solvers and related issuesp. 363
Introductionp. 363
Bandwidth reductionp. 363
Solution of linear equationsp. 366
Gauss eliminationp. 366
The conjugate gradient methodp. 367
The standard eigenvalue problemp. 372
The generalized eigenvalue problemp. 373
Sturm sequence checkp. 376
Inverse vector iterationp. 378
The subspace vectorsp. 380
The Rayleigh quotientp. 381
Subspace iterationp. 383
The Davidson algorithmp. 385
Least square residual minimizationp. 388
The Lanczos methodp. 388
Referencesp. 393
Boundary Elements
The boundary element methodp. 399
Introductionp. 399
The boundary integralp. 400
An analytical approachp. 402
A Dirichlet problemp. 402
A Neumann problemp. 406
Infinite domain Green's functionp. 408
Numerical issuesp. 414
Evaluation of the element integralsp. 414
Applying boundary conditionsp. 415
Boundary condition at the corner nodep. 417
Setting up the matrix equationp. 420
Construction of interior solutionp. 422
A worked examplep. 423
Two sum rulesp. 425
Comparing the BEM with the FEMp. 427
Problemsp. 428
Referencesp. 432
The BEM and surface plasmonsp. 435
Introductionp. 435
Multiregion BEM: two regionsp. 437
Linear interpolationp. 437
Hermite interpolationp. 439
Bulk and surface plasmonsp. 440
Bulk plasma oscillationsp. 441
Surface plasmons at a single planar interfacep. 443
Surface plasmons for slab geometryp. 447
Surface plasmons in a cylindrical wirep. 451
Two metallic wiresp. 455
Metal wire on a substratep. 458
Plasmons in other confining geometriesp. 460
Surface-enhanced Raman scatteringp. 461
Problemsp. 462
Referencesp. 468
The BEM and quantum applicationsp. 471
Introductionp. 471
2D electron waveguidesp. 471
Implementing boundary conditionsp. 477
Multiregion waveguide problemsp. 483
Multiple ports and transmissionp. 484
The BEM and 2D scatteringp. 487
Eigenvalue problems and the BEMp. 491
Quantum wiresp. 491
Hearing the shape of a drump. 495
Concluding remarks on the BEMp. 498
Problemsp. 501
Referencesp. 505
Appendices
Gauss quadraturep. 511
Introductionp. 511
Gauss-Legendre quadraturep. 511
Gauss-Legendre base points and weightsp. 513
An algorithm for adaptive quadraturep. 517
Other Gauss formulasp. 519
The Cauchy principal value of an integralp. 520
Properties of Legendre functionsp. 522
Problemsp. 524
Referencesp. 525
Generalized functionsp. 527
The Dirac [delta]-functionp. 527
The [delta]-function as the limit of a "normal" functionp. 530
[delta]-functions in three dimensionsp. 532
Other generalized functionsp. 533
The step-function [theta](x)p. 533
The sign-function [varepsilon](x)p. 534
The Plemelj formulap. 535
An integral representation for [theta](z)p. 536
Problemsp. 536
Referencesp. 538
Green's functionsp. 541
Introductionp. 541
Properties of Green's functionsp. 543
Sturm-Liouville differential operatorsp. 547
Green's functions in electrostaticsp. 554
Boundary integral solutions: a commentp. 557
Green's functions in electrodynamicsp. 565
The wave equation in one dimensionp. 570
The wave equation in two dimensionsp. 573
Green's functions and integral equationsp. 574
Problemsp. 576
Referencesp. 579
Physical constantsp. 581
Author indexp. 583
Subject indexp. 597
Table of Contents provided by Syndetics. All Rights Reserved.

책소개

Starting from a clear, concise introduction, the powerful finite element and boundary element methods of engineering are developed for application to quantum mechanics. The reader is led through illustrative examples displaying the strengths of these methods using application to fundamental quantum mechanical problems and to the design/simulation of quantum nanoscale devices.

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Ram-Mohan, L. Ramdas [저] 신작알림 SMS신청
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