Quantum Mechanics for Nanostructures

by
Format: Hardcover
Pub. Date: 2010-06-28
Publisher(s): Cambridge University Press
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Summary

The properties of new nanoscale materials, their fabrication and applications, as well as the operational principles of nanodevices and systems, are solely determined by quantum-mechanical laws and principles. This textbook introduces engineers to quantum mechanics and the world of nanostructures, enabling them to apply the theories to numerous nanostructure problems. The textbook covers the fundamentals of quantum mechanics, including uncertainty relations, the Schr_dinger equation, perturbation theory, and tunneling. These are then applied to a quantum dot, the smallest artificial atom, and compared to hydrogen, the smallest atom in nature. Nanoscale objects with higher dimensionality, such as quantum wires and quantum wells, are introduced, as well as nanoscale materials and nanodevices. Numerous examples throughout the text help students to understand the material.

Author Biography

Vladimir V. Mitin is Suny Distinguished Professor at the Department of Electrical Engineering and Adjunct Professor of Physics at the University at Buffalo, The State University of New York. He is the author of eight textbooks and monographs and more than 490 professional publications and presentations. Dmitry I. Sementsov is Professor of Physics at Ulyanovsk State University, Russia. He is the author of more than 420 papers in peer-reviewed journals. Nizami Z. Vagidov is Research Assistant Professor of Electrical Engineering at the University at Buffalo, The State University of New York. He is the author of about 90 professional publications in the fields of solid-state electronics, nanoelectronics, and nanotechnology.

Table of Contents

Prefacep. ix
List of notationp. xiii
The nanoworld and quantum physicsp. 1
A review of milestones in nanoscience and nanotechnologyp. 1
Nanostructures and quantum physicsp. 4
Layered nanostructures and superlatticesp. 8
Nanoparticles and nanoclustersp. 10
Carbon-based nanomaterialsp. 14
Wave-particle duality and its manifestation in radiation and particle behaviorp. 19
Blackbody radiation and photon gasp. 19
The quantum character of the interaction of radiation with matterp. 31
Wave properties of particlesp. 39
The uncertainty relationsp. 47
The world of the nanoscale and the wavefunctionp. 52
The Schrödinger equationp. 56
Summaryp. 63
Problemsp. 63
Layered nanostructures as the simplest systems to study electron behavior in a one-dimensional potentialp. 65
The motion of a free electron in vacuump. 66
An electron in a potential well with infinite barriersp. 69
An electron in a potential well with finite barriersp. 75
Propagation of an electron above the potential wellp. 84
Tunneling: propagation of an electron in the region of a potential barrierp. 89
Summaryp. 101
Problemsp. 101
Additional examples of quantized motionp. 105
An electron in a rectangular potential well (quantum box)p. 105
An electron in a spherically-symmetric potential wellp. 109
Quantum harmonic oscillatorsp. 115
Phononsp. 126
Summaryp. 133
Problemsp. 134
Approximate methods of finding quantum statesp. 136
Stationary perturbation theory for a system with non-degenerate statesp. 136
Stationary perturbation theory for a system with degenerate statesp. 141
Non-stationary perturbation theoryp. 142
The quasiclassical approximationp. 148
Summaryp. 151
Problemsp. 152
Quantum states in atoms and moleculesp. 155
The hydrogen atomp. 155
The emission spectrum of the hydrogen atomp. 166
The spin of an electronp. 169
Many-electron atomsp. 173
The wavefunction of a system of identical particlesp. 181
The hydrogen moleculep. 184
Summaryp. 190
Problemsp. 191
Quantization in nanostructuresp. 193
The number and density of quantum statesp. 193
Dimensional quantization and low-dimensional structuresp. 199
Quantum states of an electron in low-dimensional structuresp. 204
The number of states and density of states for nanostructuresp. 210
Double-quantum-dot structures (artificial molecules)p. 218
An electron in a periodic one-dimensional potentialp. 229
A one-dimensional superlattice of quantum dotsp. 241
A three-dimensional superlattice of quantum dotsp. 250
Summaryp. 254
Problemsp. 255
Nanostructures and their applicationsp. 258
Methods of fabrication of nanostructuresp. 258
Tools for characterization with nanoscale resolutionp. 269
Selected examples of nanodevices and systemsp. 282
Classical dynamics of particles and wavesp. 310
Classical dynamics of particlesp. 311
Oscillatory motion of a particlep. 321
Summaryp. 334
Problemsp. 335
Electromagnetic fields and wavesp. 338
Equations of an electromagnetic fieldp. 338
Electromagnetic wavesp. 345
Reflection of a plane wave from the interface between two mediap. 353
Light and its wave propertiesp. 362
Summaryp. 374
Problemsp. 375
Crystals as atomic latticesp. 378
Crystalline structuresp. 379
The nature of attraction and repulsion forcesp. 385
Degenerate electron gasp. 392
Waves in a crystalline lattice and normal coordinatesp. 396
The energy spectrum of an electron in a crystalp. 400
Electrons in semiconductorsp. 411
Summaryp. 420
Problemsp. 421
Tables of unitsp. 423
Indexp. 427
Table of Contents provided by Ingram. All Rights Reserved.

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