Quantum Nature of the Nanoworld

4.1 Bohrs Model of the Nuclear Atom 48

4.1.1 Quantization of Angular Momentum 48

4.1.2 Extensions of Bohrs Model 49

4.2 Particle-wave Nature of Light and Matter, DeBroglie Formulas A= h/p, E=hv 50

4.3 Wavefunction Wfor Electron, Probability Density W*W, Traveling and Standing Waves 51

4.4 Maxwells Equations; E and B as Wavefunctions for Photons, Optical Fiber Modes 52

4.5 The Heisenberg Uncertainty Principle 53

4.6 Schrodinger Equation, Quantum States and Energies, Barrier Tunneling 54

4.6.1 Schrodinger Equations in one Dimension 55

4.6.2 The Trapped Particle in one Dimension 56

4.6.3 Reflection and Tunneling at a Potential Step 58

4.6.4 Penetration of a Barrier 60

4.6.5 Trapped Particles in Two and Three Dimensions: Quantum Dot 61

4.6.6 2D Bands and Quantum Wires 63

4.6.7 The Simple Harmonic Oscillator 65

4.6.8 Schrodinger Equation in Spherical Polar Coordinates 66

4.7 The Hydrogen Atom, One-electron Atoms, Excitons 66

4.8 Fermions, Bosons and Occupation Rules 72

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