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10 videos · 5 h 22 min
Course · Oxford
University of Oxford · James Binney · 2009–10
James Binney's Oxford course, given over Michaelmas Term 2009 and Hilary Term 2010 and built on probability amplitudes and Dirac notation from the very first lecture. Highlights: tunnelling and radioactive decay, the EPR argument and Bell's inequality, spin and the Stern–Gerlach experiment, and a full treatment of hydrogen.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach · 2013
Barton Zwiebach's lecture from MIT's 8.05 Quantum Physics II (Fall 2013) builds Dirac's notation from the inner product upward: bras and kets, projection operators, the adjoint of an operator, Hermitian and unitary operators, and the uncertainty of a Hermitian operator. It runs well ahead of this course, so treat it as a view of where today's grammar leads.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach
Zwiebach on what makes Hermitian operators special. They always have enough eigenfunctions to span the whole space of states (the spectral theorem), and eigenfunctions with different eigenvalues are automatically orthogonal: two of section 3's three guarantees. Watch how he handles degenerate eigenvalues (from 10:52), where an orthonormal set has to be chosen rather than coming for free.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach
Zwiebach writes down the Pauli matrices, multiplies σ1 and σ2 in both orders and finds the commutator 2iσ3, section 6's cycle. He then states, without proof, that no two matrices can have a plain number as their commutator, so matrices for x and p must be infinite-dimensional; section 7's callout gives the trace argument he leaves to you. From 6:07 he moves to the Schrödinger equation in three dimensions, ending with the commutators of the x, y and z positions and momenta.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach
Zwiebach adds a potential to build the general Schrödinger equation, defines the position operator x̂, then lets x̂p̂ − p̂x̂ act on a test function: the same product-rule calculation as section 7, ending in iħ. Note his remark that this is the road Heisenberg took into quantum mechanics, through operators and their commutators rather than a wave equation.
Lecture · MIT
MIT OpenCourseWare · David Kaiser
MIT physicist and historian David Kaiser on quantum numbers and spin, Heisenberg and matrix mechanics, and the uncertainty principle. This link starts at the 'Matrix mechanics' chapter (39:39), the human story behind sections 6 and 7, and 'Uncertainty principle' follows at 54:08. Rewind to the start for the background: old quantum theory, the anomalous Zeeman effect, and spin.
Lecture · MIT
MIT OpenCourseWare · Allan Adams · 2013
The lecture from MIT 8.04 Quantum Physics I (Allan Adams, 2013) that goes with Chapter 14. The whole course is in the Lecture Hall.
Course · MIT
MIT OpenCourseWare · Allan Adams · 2013
Allan Adams' celebrated course starts from superposition and the experimental facts, builds the wavefunction, operators and the Schrödinger equation, then tours scattering, hydrogen, identical particles and band structure before closing on entanglement and Bell's theorem. Calculus and a little linear algebra are enough to keep up.
Explainer · YouTube
Parth G
Parth G explains what a quantum operator is and why commutators, which measure whether the order of two operations matters, are so useful, including their role in Ehrenfest's theorem. Watch it first, then come back to see the same ideas written in Dirac's notation and worked through with real two-by-two matrices.
Explainer · YouTube
3Blue1Brown
Not a quantum video, but the clearest picture anywhere of what an eigenvector is: a direction that a transformation only stretches, squashes or flips, never turns. Hold that image through the session, because a quantum eigenstate is exactly such a direction, and its eigenvalue is a possible measurement result.