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10 videos · 6 h 32 min
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.
Course · Stanford
Stanford · Leonard Susskind · 2012
Leonard Susskind's course for curious adults, the basis of his book with Art Friedman. It starts from a single spin, builds states, operators and measurement from scratch, then reaches entanglement — one of the cleanest routes from zero to the real formalism.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach · 2013
The lecture from MIT 8.05 Quantum Physics II (Barton Zwiebach, 2013) that goes with Chapter 8. The whole course is in the Lecture Hall.
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
A ten-minute segment of MIT 8.04 (Spring 2016) that defines the Δ precisely: the standard deviation of an observable in a given state, built from expectation values. It is this section's ensemble definition on the blackboard, a property of the state rather than of any one blurry measurement.
Lecture · MIT
MIT OpenCourseWare · Barton Zwiebach
MIT 8.05, the lecture after the one in the Lecture Hall. It opens on the energy-time relation, read as this section reads it: Δt is how fast a state can change, not a spread of clock readings. Zwiebach then uses the uncertainty principle to put a floor under a ground-state energy, section 6's argument made rigorous. The second half, on diagonalizing operators, is chapter 14 material.
Lecture · MIT
MIT OpenCourseWare · Allan Adams · 2013
The lecture from MIT 8.04 Quantum Physics I (Allan Adams, 2013) that goes with Chapter 8. The whole course is in the Lecture Hall.
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.