Leonard Susskind Quantum Entanglement Lecture 2006

Quantum Entanglement Lecture 02 notes 2006-10-02

 measuring electron spin:….

 .. Dirac notation;….

probability of a vector….

Hermitian matrix (a matrix of observables)

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Quantum Entanglement Lecture 3  2006-10-09….

Quantum Mechanics  is calculation of probabilities….

sigma matrices….

observables, eigenvalues and eigenvectors are orthogonal….

can measure component of electron spin in any x,y,z….

example, unit pointer in any arbitrary direction.

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Quantum Entanglement Lecture 4  2006-10-16….

                Review: completion of single bit system….

                probability of finding an electron in a particular state….

                calculate eigenvectors of σ.n….

                notes on preparing and measuring a system (not in video)….

                simultaneous measurement

                entanglement – simple definition….

                entangled state, prepared together….

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Quantum Entanglement Lecture 5  2006-10-23….

                review action on sigma matrices….

                the expectation value for all sigma observable directions is zero (50% up, 50% down)….

                which + or – is an eigenvector of the entangled state – the singlet state….

                Bell’s Theorem (a classical probability theorem)….

                Bell’s Theorem not true in entangled state….

                Calculate sigma projection operators….

                alternate definition of probability using projection operators….

proof you cannot clone a quantum system….

               Download Notes:Quantum-Entanglement-Notes-lecture-5-20061023

Quantum Entanglement Lecture 6  2006-10-30….

                review of entangled states, sub-spaces….

                review of projection operators, probabilities….

                review: classical probability (Bell’s)….

the 2 slit experiment, one hole, two hole….

Destructive interference of a reording device….

Entanglement of the experiment with an apparatus

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Quantum Entanglement Lecture 7  2006-11-06….

                review 2 slit experiment….

                                formal calculation of probability that electron found at m….

                                destroying the interference pattern….

                Schrodinger's cat is not in a superposition of alive and dead….

                classical entropy….

                Trace of a matrix….

                quantum density matrix….

Quantum mechanical entropy of a density matrix….

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Quantum Entanglement Lecture 8  2006-11-12….

Density matrix: a more general way to make probability statements about a system….

                classical definition of entropy, probabilities….

                entanglement and unentangled probabilities….

                how states change with time….

                H is called the Hamiltonian, it is Hermitian, and an observable, the energy of the system.

                entrop

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Quantum Entanglement Lecture 9  2006-11-27….

                review – how things change with time….

            The Schrodinger equation

                Einstein’s photon equation

                vector that is the sum of eigenvectors of the Hamiltonian….

                what is the time derivative of the average of the Hamiltonian itself? zero….

                Spin in a magnetic field….

                energy states with 2 electrons….

y is the measure of entanglement?

               Download Notes:Quantum-Entanglement-Notes-lecture-9-20061127