Quantum Mechanics
Quantum Mechanics (Winter 2012, Standard Univ.). Instructor: Professor Leonard Susskind. Quantum theory governs the universe at its most basic level. In the first half of the 20th century physics was turned on its head by the radical discoveries of Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schrodinger. An entire new logical and mathematical foundation - quantum mechanics - eventually replaced classical physics. We will explore the quantum world, including the particle theory of light, the Heisenberg Uncertainty Principle, and the Schrodinger Equation. (from theoreticalminimum.com)
| Lecture 01 - Introduction to Quantum Mechanics The non-intuitive logic of quantum mechanics, Vector spaces, Rules for updating states, Quantum preparation and measurement are the same operation, Mathematics of abstract vector spaces. |
| Lecture 02 - The basic logic of quantum mechanics Single spin system, Basic logic of quantum mechanics, Vector spaces, Basis vectors, Analogy between vector space and configuration space. |
| Lecture 03 - Vector spaces and operators Vector spaces and state vectors, Hermitian operators and observables, Eigenvectors and eigenvalues, Normalization and phase factors, Operators for a single spin system, Pauli matrices. |
| Lecture 04 - Time evolution of a quantum system Four fundamental principles of quantum mechanics, Unitarity and unitary evolution of a system, Derivation of the time-dependent Schrodinger equation, Time evolution of expectation value. |
| Lecture 05 - Uncertainty, unitary evolution, and Schrodinger equation Heisenberg uncertainty principle, Commutator, Time evolution of a system, Quantum mechanical Hamiltonian, Solving the Schrodinger equation, Expectation values of observables. |
| Lecture 06 - Entanglement Wave function collapse, Tensor products, Product states, Entanglement, Observables for entangled states, Expectation values of entangled states, Singlet and triplet states. |
| Lecture 07 - Entanglement and the nature of reality Quantum wave function, Product vs. entangled states, Maximum entanglement, Density matrices, Measurement, Spooky action at a distance, Computer simulation of product and entangled states. |
| Lecture 08 - Particles moving in one dimension and their operators Is entanglement reversible? Continuous systems, A particle moving in one dimension, Position, momentum, and energy operators, Hamiltonian operator generates the time evolution of a system. |
| Lecture 09 - Fourier analysis applied to quantum mechanics and the uncertainty principle Triplet state decay, Fourier analysis applied to quantum mechanics, Relationship between the Fourier transform and the uncertainty principle. |
| Lecture 10 - The uncertainty principle and classical analogs Derivation of the uncertainty principle, Using the Schrodinger equation to derive the classical equations of motion for a wave packet, Wave packets. |
| References |
| Quantum Mechanics (Winter, 2012) | The Theoretical Minimum We will explore the quantum world, including the particle theory of light, the Heisenberg Uncertainty Principle, and the Schrodinger Equation. |