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lec #
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topics
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Lecture 1: An overview of quantum mechanics.
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L1.1
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Quantum mechanics as a framework. Defining linearity (17:46)
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L1.2
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Linearity and nonlinear theories. Schrödinger’s equation (10:01)
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L1.3
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Necessity of complex numbers (07:38)
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L1.4
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Photons and the loss of determinism (17:20)
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L1.5
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The nature of superposition. Mach-Zehnder interferometer (14:30)
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Lecture 2: Overview of quantum mechanics (cont.). Interaction-free measurements.
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L2.1
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More on superposition. General state of a photon and spin states (17:10)
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L2.2
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Entanglement (13:07)
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L2.3
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Mach-Zehnder interferometers and beam splitters (15:32)
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L2.4
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Interferometer and interference (12:26)
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L2.5
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Elitzur-Vaidman bombs (10:29)
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Lecture 3: Photoelectric effect, Compton scattering, and de Broglie wavelength.
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L3.1
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The photoelectric effect (22:54)
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L3.2
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Units of h and Compton wavelength of particles (12:39)
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L3.3
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Compton Scattering (22:34)
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L3.4
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de Broglie’s proposal (10:39)
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Lecture 4: de Broglie matter waves. Group velocity and stationary phase. Wave for a free particle.
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L4.1
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de Broglie wavelength in different frames (14:53)
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L4.2
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Galilean transformation of ordinary waves (12:16)
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L4.3
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The frequency of a matter wave (10:23)
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L4.4
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Group velocity and stationary phase approximation (10:32)
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L4.5
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Motion of a wave-packet (08:58)
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L4.6
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The wave for a free particle (14:35)
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Lecture 5: Momentum operator, Schrödinger equation, and interpretation of the wavefunction.
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L5.1
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Momentum operator, energy operator, and a differential equation (20:33)
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L5.2
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Free Schrödinger equation (09:56)
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L5.3
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The general Schrödinger equation. x, p commutator (17:58)
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L5.4
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Commutators, matrices, and 3-dimensional Schrödinger equation (16:12)
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L5.5
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Interpretation of the wavefunction (08:01)
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Lecture 6: Probability density and current. Hermitian conjugation.
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L6.1
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Normalizable wavefunctions and the question of time evolution (16:50)
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L6.2
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Is probability conserved? Hermiticity of the Hamiltonian (20:42)
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L6.3
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Probability current and current conservation (15:14)
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L6.4
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Three dimensional current and conservation (18:13)
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Lecture 7: Wavepackets and uncertainty. Time evolution and shape change time evolutions.
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L7.1
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Wavepackets and Fourier representation (12:23)
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L7.2
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Reality condition in Fourier transforms (09:11)
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L7.3
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Widths and uncertainties (19:13)
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L7.4
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Shape changes in a wave (16:56)
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L7.5
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Time evolution of a free particle wavepacket (09:44)
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Lecture 8: Uncovering momentum space. Expectation values and their time dependence.
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L8.1
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Fourier transforms and delta functions (13:58)
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L8.2
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Parseval identity (15:50)
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L8.3
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Three-dimensional Fourier transforms (06:04)
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L8.4
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Expectation values of operators (28:15)
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L8.5
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Time dependence of expectation values (7:37)
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Lecture 9: Observables, Hermitian operators, measurement and uncertainty. Particle on a circle.
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L9.1
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Expectation value of Hermitian operators (16:40)
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L9.2
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Eigenfunctions of a Hermitian operator (13:05)
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L9.3
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Completeness of eigenvectors and measurement postulate (16:56)
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L9.4
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Consistency condition. Particle on a circle (17:45)
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L9.5
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Defining uncertainty (10:31)
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