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LEC #
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TOPICS
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Part 1: Basic Concepts
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1
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Key Features of Quantum Mechanics: Linearity of the Equations of Motion, Complex Numbers are Essential, Loss of Determinism, Quantum Superpositions, Entanglement (PDF)
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2
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Experiments with Photons: Mach-Zehder Interferometer, Elitzur-Vaidman Bombs (PDF)
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3
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Particle Nature of Light and Wave Nature of Matter: Photoelectric Effect, Compton Scattering, Matter Waves (PDF)
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4
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de Broglie Wavelength and Galilean Transformations, Phase and Group Velocities, Choosing the Wavefunction for a Free Particle (PDF)
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5
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Equations for a Wavefunction, Schrödinger Equation for Particle in a Potential, Interpreting the Wavefunction (PDF)
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6
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Normalization and Time Evolution, The Wavefunction as a Probability Amplitude, The Probability Current, Probability Current in 3D and Current Conservation (PDF)
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7
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Wavepackets and Uncertainty, Wavepacket Shape Changes, Time Evolution of a Free Wave Packet (PDF)
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8
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Uncovering Momentum Space, Expectation Values of Operators, Time Dependence of Expectation Values (PDF)
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9
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Observables and Hermitian Operators, Uncertainty (PDF)
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Part 2: Quantum Physics in One-dimensional Potentials
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10
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Solving the Time-Independent Schrödinger Equation: Stationary States, Solving for Energy Eigenstates, Free Particle on a Circle (PDF)
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11
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The Infinite Square Well, The Finite Square Well (PDF)
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12
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General Properties, Bound States in Slowly Varying Potentials, Sketching Wavefunction Behavior in Different Regions, Shooting Method (PDF - 1.4MB)
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13
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Delta Function Potential, The Node Theorem, Simple Harmonic Oscillator (PDF - 1.3MB)
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14 & 15
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Algebraic Approach to the Simple Harmonic Oscillator: Algebraic Solution of the Oscillator, Operator Manipulation and the Spectrum (PDF)
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16
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Scattering States and the Step Potential: The Step Potential, Step Potential with E > V{{< sub “0” >}}, Step Potential with E < V{{< sub “0” >}}, Wavepackets in the Step Potential (PDF)
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17
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Resonant Transmission in a Square Well, The Ramsauer–Townsend Effect (PDF)
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18
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Scattering in One Dimension: Time Delay, An Example (PDF)
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Part 3: One-dimensional Scattering, Angular Momentum, and Central Potentials
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19
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Levinson’s Theorem, Resonances, Modeling the Resonance (PDF - 1.1MB)
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20 & 21
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Quantum Mechanics in 3D and Central Potentials: Schrödinger Equation in 3D and Angular Momentum, The Angular Momentum Operator, Eigenstates of Angular Momentum, The Radial Wave Equation (PDF)
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21 & 22
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Hydrogen Atom, Hydrogen Atom Spectrum (PDF)
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