| Foreword |
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| About the Authors |
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| Part I Practical Quantum Mechanics |
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1 | (94) |
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3 | (24) |
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I.1.1 Eigenvalues, eigenvector of linear operators |
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6 | (1) |
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7 | (1) |
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I.1.3 Hermitian operators: observables |
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8 | (1) |
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8 | (1) |
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9 | (1) |
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I.1.6 Commuting operators |
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9 | (4) |
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I.1.7 Two important examples of non-commuting operators |
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13 | (1) |
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I.1.8 Heisenberg inequalities |
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14 | (1) |
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15 | (1) |
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I.1.10 Spin-orbit coupling |
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16 | (1) |
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17 | (3) |
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I.1.12 Identical particles and Pauli principle |
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20 | (4) |
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I.1.13 Tensorial products |
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24 | (3) |
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I.2 Bound and Extended States |
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27 | (30) |
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I.2.1 Propagating and evanescent states |
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27 | (3) |
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I.2.2 Probability current |
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30 | (1) |
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I.2.3 Boundary conditions |
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31 | (8) |
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39 | (9) |
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I.2.5 The problem of plane waves |
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48 | (4) |
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I.2.6 Schrodinger equation, time-dependent aspects |
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52 | (5) |
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57 | (38) |
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57 | (3) |
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I.3.2 Perturbation theory |
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60 | (10) |
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I.3.2.1 Non-degenerate perturbation theory |
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62 | (5) |
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I.3.2.2 Degenerate perturbation theory |
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67 | (3) |
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I.3.3 Time-dependent perturbation theory |
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70 | (13) |
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I.3.3.1 Static scatterers |
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71 | (6) |
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I.3.3.2 Time-dependent scattering |
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77 | (6) |
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I.4 Landau Quantisation of Electron Motion in Ideal Semiconductor Bulks and Heterostructures |
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83 | (20) |
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I.4.1 Landau level degeneracy |
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88 | (1) |
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I.4.2 Perturbative estimates of deltaH1 and deltaH2 |
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89 | (2) |
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I.4.3 Magnetic field-dependent density of states |
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91 | (2) |
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I.4.4 A tractable case of lifting of the ky degeneracy: the crossed E, B fields |
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93 | (2) |
| Part II The Physics of Heterostructures |
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95 | (160) |
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II.1 Background on Heterostructures |
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97 | (6) |
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II.2 Electrons States in Nanostructures |
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103 | (36) |
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II.2.1 The envelope function approximation |
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103 | (17) |
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103 | (5) |
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II.2.1.2 Electronic states in bulk semiconductors |
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108 | (7) |
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II.2.1.3 Heterostructure states |
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115 | (5) |
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II.2.2 Multiple quantum wells: transfer matrix method |
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120 | (6) |
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II.2.2.1 Multiple quantum wells and superlattices |
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120 | (2) |
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II.2.2.2 Transfer matrix method |
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122 | (4) |
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II.2.3 Double quantum wells |
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126 | (9) |
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II.2.3.1 Tight binding analysis |
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131 | (3) |
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II.2.3.2 Symmetrical double quantum well |
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134 | (1) |
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135 | (4) |
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II.3 Beyond the Ideal World |
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139 | (26) |
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II.3.1 Population, velocity, energy relaxation times through rate equations |
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147 | (4) |
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II.3.2 Rate equations with elastic and inelastic processes |
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151 | (3) |
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II.3.3 Analysis of the relaxation times in rate equations |
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154 | (8) |
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II.3.3.1 Impurity form factor |
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155 | (3) |
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II.3.3.2 Phonon form factors and transition rates |
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158 | (4) |
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II.3.4 Consequence of the Born approximation on the additivity of scattering frequencies |
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162 | (3) |
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II.4 Screening at the Semi-classical Approximation |
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165 | (12) |
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II.4.1 Case of a single subband occupation |
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166 | (5) |
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II.4.2 Case of many subbands occupation |
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171 | (2) |
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II.4.3 Screening of inter-subband matrix elements |
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173 | (4) |
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II.5 Results for Static Scatterers |
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177 | (46) |
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II.5.1 Scattering by static disorder |
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177 | (7) |
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II.5.2 Scattering of composite particles/excitons at the Born approximation |
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184 | (9) |
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II.5.3 Scattering on magnetic impurities |
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193 | (12) |
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II.5.3.1 The "spin"-flip scattering of electrons |
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193 | (8) |
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II.5.3.2 The "spin"-flip scattering of holes |
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201 | (4) |
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II.5.4 Three-body collisions |
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205 | (18) |
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II.5.4.1 FCA in imperfect bulks and heterostructures |
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206 | (12) |
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II.5.4.2 Phonon scattering in the presence of static scatterers |
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218 | (5) |
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II.6 Results for Electron-Phonon Interaction |
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223 | (12) |
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II.6.1 Optical phonon scattering |
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224 | (5) |
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II.6.2 Acoustical phonon scattering |
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229 | (2) |
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231 | (4) |
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II.7 Beyond the Born Approximation |
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235 | (20) |
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II.7.1 Scattering between Landau levels |
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238 | (17) |
| Part III Exercises |
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255 | (168) |
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1 Average position and velocity |
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257 | (1) |
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2 Average velocity in a bound state |
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257 | (1) |
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258 | (2) |
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4 Density of states of a camel back shaped dispersion relation |
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260 | (3) |
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5 Heisenberg inequality in a quantum well with infinitely high barriers |
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263 | (3) |
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6 Manipulating Slater determinants |
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266 | (1) |
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7 Pauli principle for two weakly interacting electrons in 1D |
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267 | (3) |
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8 Calculation with Pauli matrices |
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270 | (1) |
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9 Moss-Burstein shift of interband absorption |
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271 | (2) |
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273 | (3) |
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11 Absence of degeneracy for the 1D bound states |
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276 | (2) |
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12 Variational method: hydrogen atom |
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278 | (1) |
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13 Variational method: electron in a triangular potential |
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279 | (1) |
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14 Variational method: anharmonic oscillator |
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280 | (1) |
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15 Screened coulombic bound states |
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281 | (6) |
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16 A two-dimensional coulombic problem |
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287 | (3) |
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17 Inter-subband transitions in cubic GaN/AlN quantum wells: information on the conduction band offset |
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290 | (4) |
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18 Asymmetrical square quantum well |
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294 | (2) |
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19 Spherical quantum dots |
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296 | (2) |
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298 | (4) |
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21 Wavefunction amplitude at the interfaces |
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302 | (2) |
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22 Interface state in HgTe/CdTe heterojunctions |
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304 | (2) |
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306 | (7) |
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24 Application of the Bohr-Sommerfeld quantisation rule to 1D confining potential: digital alloying |
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313 | (6) |
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25 Transmission/reflection in a delta quantum well |
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319 | (4) |
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26 Static perturbation of a harmonic oscillator |
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323 | (1) |
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27 Static perturbation (degenerate case) |
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324 | (1) |
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28 Degenerate perturbation calculus applied to quantum dots with cylindrical symmetry |
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325 | (2) |
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29 Quantum well and a delta potential: perturbative estimate |
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327 | (5) |
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30 Quantum dot anisotropy |
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332 | (7) |
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31 Defect in a superlattice: tight binding approach |
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339 | (6) |
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32 Bound states created by two delta scatterers in a Landau level |
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345 | (6) |
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33 Time-dependent evolution in an infinitely deep quantum well |
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351 | (1) |
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34 Time-dependent problem: evolution |
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352 | (4) |
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35 A touch of interaction representation |
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356 | (1) |
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36 Time evolution if A and H commute |
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357 | (1) |
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37 Oscillator: time evolution of averages |
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358 | (1) |
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38 Time evolution of a system where one level is coupled to N degenerate levels |
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359 | (4) |
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39 Time-dependent Hamiltonian: an exactly solvable model |
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363 | (2) |
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40 Time evolution of superlattice states |
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365 | (5) |
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370 | (2) |
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42 Average velocity of a wavepacket |
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372 | (1) |
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43 Time-dependent perturbation in a 2-level system |
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373 | (2) |
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44 Universal absorption probability for interband transitions in graphene |
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375 | (8) |
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45 Scattering by N random impurity dimmers |
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383 | (5) |
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46 A tractable example of selective doping by delta scatterers |
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388 | (3) |
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47 Comparison between Born and self-consistent Born approximations |
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391 | (5) |
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48 Influence of a fast emptying of the final subband on the equilibrium between two subbands |
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396 | (2) |
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49 Phonon-mediated equilibration of the electronic temperature to the lattice temperature |
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398 | (4) |
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50 Inter-subband scattering by unscreened coulombic impurities |
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402 | (5) |
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51 Evaluation of a double sum appearing in the free carrier absorption |
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407 | (3) |
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52 Energy loss rate for the in-plane polarisation T = 0 K |
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410 | (3) |
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53 Inter-subband absorption versus carrier concentration in an ideal heterostructure |
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413 | (3) |
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54 Electron-LO phonon interaction: dimensionality dependence |
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416 | (7) |
| Bibliography |
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423 | (6) |
| Index |
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429 | |
