Lecture 3. Observables

0:00 Observables in quantum mechanics are self-adjoint operators 9:39 Eigenvalues and eigenvectors of self-adjoint operators 19:43 Spectral Theorem for self-adjoint operators 24:43 Bra-Ket notation 29:05 Measuring polarization of a photon 37:42 Measuring spin of an electron 41:40 General axiomatics of measurements in quantum mechanics 52:03 Measuring qubits in quantum computing 1:01:05 Coordinate and momentum as observables for a particle in a potential well 1:13:36 When two observables may be measured simultaneously In this lecture we discuss measurements in quantum mechanics and the notion of an observable, which is a self-adjoint operator on the space of quantum states. The outcome of the measurement procedure is probabilistic, and it changes the state of the quantum system. This is a lecture in the course on "Quantum Computing". My book "Quantum Computing for High School Students" is available here: https://qubitpublishing.com/ or from Amazon. Complete playlist for this course: https://www.youtube.com/playlist?list=PLu6jbin1VpDD87rdSDF4HRfITWF_LwgOx