Quantum Mechanics
Quantum Mechanics (Winter 2008, 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 | Quantum Mechanics (Winter 2008) Intro, Two Slit Experiment, Uncertainty - two slit experiment, discussions on classical quantum behavior, uncertainty principle, vector spaces over the complex numbers. |
| Lecture 02 | Quantum Mechanics (Winter 2008) Vector Review, Basis, Dyads, Spaces - review of complex numbers, complex vector space, basis vectors, physical significance of spaces. |
| Lecture 03 | Quantum Mechanics (Winter 2008) Operators, Observables, Dirac Delta, Hermitian, Anti-Hermitian - mathematics of linear operators, Hermitian operators, postulates of quantum mechanics, Dirac's delta function. |
| Lecture 04 | Quantum Mechanics (Winter 2008) Probabilities, Momentum, Slit Experiment - the Dirac delta function, rules of probabilities for quantum mechanics, momentum of a particle moving on a circle, slit experiment review. |
| Lecture 05 | Quantum Mechanics (Winter 2008) Wave Function, Fourier Transform, Polarized Photon - integer periodicity of the wave function, identity operator, Fourier transform between momentum and position states. |
| Lecture 06 | Quantum Mechanics (Winter 2008) Photon Polarization, Circular, Angles, Hermitian, Probability - polarization at an arbitrary angle, polarization with imaginary numbers, expectation value. |
| Lecture 07 | Quantum Mechanics (Winter 2008) Photon Elliptical Polarization, Phase Change, Unitary Operator - Hermitian operators, multiplication by a phase, change of state with time, mathematics of unitary operators. |
| Lecture 08 | Quantum Mechanics (Winter 2008) Time Evaluation, Unitary, Hamiltonian, Schrodinger - classical: Hamiltonian, Poisson brackets, example: time evaluation of photon polarization, time evaluation of expectation value. |
| Lecture 09 | Quantum Mechanics (Winter 2008) Schrodinger Derivation, Commutators, Poisson brackets, Black Body Radiation. |
| Lecture 10 | Quantum Mechanics (Winter 2008) Harmonic Oscillator, Creation, Annihilation Operators. |
| References |
| Quantum Mechanics (Winter, 2008) | The Theoretical Minimum We will explore the quantum world, including the particle theory of light, the Heisenberg Uncertainty Principle, and the Schrodinger Equation. |