Quantum Physics in the Nanoworld

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1 Hans Lüth Quantum Physics in the Nanoworld Schrödinger's Cat and the Dwarfs 4) Springer

2 Contents 1 Introduction General and Historical Remarks Importance for Science and Technology Philosophical Implications 5 References 8 2 Some Fundamental Experiments Photoelectric Effect Compton Effect Diffraction of Massive Particles Particle Interference at the Double Slit Double Slit Experiments with Electrons Particle Interference and "Which-Way" Information 23 References 25 3 Particle -Wave Duality The Wave Function and Its Interpretation Wave Packet and Particle Velocity The Uncertainty Principle An Excursion into Classical Mechanics Observables, Operators and Schrödinger Equation Simple Solutions of the Schrödinger Equation "Locked-Up" Electrons: Confined Quantum States Particle Currents Electrons Run Against a Potential Step Electrons Tunnel Through a Barrier Resonant Tunneling Single Electron Tunneling 72 References 78 4 Quantum States in Hilbert Space Eigenvectors and Measurement of Observables 79 ix

3 x Contents 4.2 Commutation of Operators: Commutators Representation of Quantum States and Observables Vectors of Probability Amplitudes and Matrices as Operators Rotations of Hilbert Space Quantum States in Dirac Notation Quantum States with a Continuous Eigenvalue Spectrum Time Evolution in Quantum Mechanics Garnes with Operators: The Oscillator The Classical Harmonic Oscillator Upstairs-Downstairs: Step Operators and Eigenvalues The Anharmonic Oscillator 115 References Angular Momentum, Spin and Particle Categories The Classical Circular Motion Quantum Mechanical Angular Momentum Rotational Symmetry and Angular Momentum; Eigenstates Circulating Electrons in a Magnetic Field The Lorentz Force The Hamilton Operator with Magnetic Field Angular Momentum and Magnetic Moment Gauge Invariance and Aharanov Bohm-Effect The Spin Stern Gerlach Experiment The Spin and Its 2D Hilbert Space Spin Precession Particle Categories: Fermions and Bosons Two and More Particles Spin and Particle Categories: The Pauli Exclusion Principle Two Different Worlds: Fermi and Bose Statistics The Zoo of Elementary Particles Angular Momentum in Nanostructures and Atoms Artificial Quantum Dot Atoms Atoms and Periodic Table Quantum Rings 196 References Approximate Solutions for Important Model Systems Particles in a Weakly Varying Potential: The WKB Method Application: Tunneling Through a Schottky Barrier Clever Guess of a Wave Function: The Variational Method Example of the Harmonic Oscillator The Ground State of the Hydrogen Atom Molecules and Coupled Quantum Dots 215

4 Contents xi 6.3 Small Stationary Potential Perturbations: The Time-Independent Perturbation Method Perturbation of Degenerate States Example: The Stark Effect in a Semiconductor Quantum Well Transitions Between Quantum States: The Time-Dependent Perturbation Method Periodic Perturbation: Fermi's Golden Rule Electron Light Interaction: Optical Transitions Optical Absorption and Emission in a Quantum Well Dipole Selection Rules for Angular Momentum States Electronic Transitions in 2-Level Systems: The Rotating Wave Approximation Level Systems in Resonance with Electromagnetic Radiation Spin Flip Nuclear Spin Resonance in Chemistry, Biology and Medicine Scattering of Particles Scattered Waves and Differential Scattering Cross Section Scattering Amplitude and Born Approximation Coulomb Scattering Scattering on Crystals, on Surfaces and on Nanostructures Inelastic Scattering on a Molecule 285 References Superposition, Entanglement and Other Oddities Superposition of Quantum States Scattering of Two Identical Particles: A Special Superposition State Entanglement Bell's Inequality and Its Experimental Check "Which Way" Information and Entanglement: A Gedanken Experiment Pure and Mixed States: The Density Matrix Quantum Mechanical and Classical Probabilities The Density Matrix Quantum Environment, Measurement Process and Entanglement Subsystem and Environment Open Quantum Systems, Decoherence and Measurement Process Schrödinger's Cat Superposition States for Quantum-Bits and Quantum Computing Coupled Quantum Dots as Quantum-Bits 331

5 xii Contents Experimental Realization of a Quantum-Bit by Quantum Dots 335 References Fields and Quanta Ingredients of a Quantum Field Theory Quantization of the Electromagnetic Field What are Photons' Level Atom in the Light Field: Spontaneous Emission Atom Diffraction by Light Waves Once Again: "Which Way" Information and Entanglement The Casimir Effect The Quantized Schrödinger Field of Massive Particles The Quantized Fermionic Schrödinger Field Field Operators and Back to the Single Particle Schrödinger Equation Electrons in Crystals: Back to the Single Particle Approximation The Band Model: Metals and Semiconductors Quantized Lattice Waves: Phonons Phonon Phonon Interaction Electron Phonon Interaction Absorption and Emission of Phonons Field Quanta Mediate Forces Between Particles 423 References Synopsis 429 Appendix A Interfaces and Heterostructures 433 Appendix B Preparation of Semiconductor Nanostructures 439 References 447 Appendix C The Reduced Density Matrix 449 Problems 453 Problems to Chap Problems to Chap Problems to Chap Problems to Chap Problems to Chap Problems to Chap Index 463

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer

QUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer Franz Schwabl QUANTUM MECHANICS Translated by Ronald Kates Second Revised Edition With 122Figures, 16Tables, Numerous Worked Examples, and 126 Problems ff Springer Contents 1. Historical and Experimental