## Quantum Entanglements, Part 1

**Quantum Entanglements, Part 1 (Fall 2006, Stanford Univ.)**. Instructor: Professor Leonard Susskind. The old Copenhagen interpretation of quantum mechanics
associated with Niels Bohr is giving way to a more profound interpretation based on the idea of quantum entanglement. Entanglement not only replaces
the obsolete notion of the collapse of the wave function but it is also the basis for Bell's famous theorem, the new paradigm of quantum computing,
and finally the widely discussed "many-worlds" interpretation of quantum mechanics originated by Everett.
(from **theoreticalminimum.com**)

Lecture 1 | Quantum Entanglements (Fall 2006)A basic definition of what constitutes a physics system, a classical system and a quantum system. |

Lecture 2 | Quantum Entanglements (Fall 2006)Electron spin, Concepts of quantum states and observables, Classical states and observables. |

Lecture 3 | Quantum Entanglements (Fall 2006)Hermitian matrices, Two-dimensional Hermitian matrices, Quantum observables, Spin operators. |

Lecture 4 | Quantum Entanglements (Fall 2006)This lecture generalises the definition of spin operators of a single electron in the three spatial directions to a spin in any direction. |

Lecture 5 | Quantum Entanglements (Fall 2006)Example states (non-entangled States, entangled states, singlet state), Projection operators, Violation of Bell's Theorem, Time evolution postulate. |

Lecture 6 | Quantum Entanglements (Fall 2006)Review of projection operators, The singlet state, Two-slit experiment. |

Lecture 7 | Quantum Entanglements (Fall 2006)Two-slit experiment; measurement at quantum level, Introduction to entropy, Quantum density matrix, Quantum entropy. |

Lecture 8 | Quantum Entanglements (Fall 2006)Pure and mixed states, Composite systems, Examples of composite states, Time evolution of states. |

Lecture 9 | Quantum Entanglements (Fall 2006)Solutions to Schrodinger's equation, Time evolution of observables, Spin in a magnetic field, Time evolution of a pair of electrons. |

References |

Quantum Entanglement (Fall, 2006) | The Theoretical MinimumThe old Copenhagen interpretation of quantum mechanics associated with Niels Bohr is giving way to a more profound interpretation based on the idea of quantum entanglement. |

Quantum Entanglements Lecture NotesQuantum Entanglements. Professor Leonard Susskind. This course is an introduction to quantum mechanics. |