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Brilliant

Quantum Objects

via Brilliant

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Overview

The principles of quantum mechanics came from investigating microscopic phenomena; the bizarre behavior of quantum objects like atoms and elementary particles that often appear to contradict classical mechanics and probability.

In this course you'll explore experiments of quantum objects and use them to construct new equations of motion, new laws of physics, and a new system of measurement based not on numbers, but on algebras. By the end, you’ll gain a new appreciation for how the physics of the small enables lasers, transistors and other modern technologies that define our world. Then you'll be ready to dive into the ongoing revolution of quantum information and computing.

Syllabus

  • Spin Class: Get to know the rules of quantum objects by exploring the strange behavior of spinning particles.
    • Why Quantum?: Tiny objects don't just bounce off walls, and even after you sort them they still end up mixed up.
    • Classical Expectations: With a couple magnets and a source of neutrons, you can observe the most quantum property of all: spin.
    • Quantum Surprises: The Stern-Gerlach experiment reveals that subatomic particles are spinning like tops — or are they?
    • Observables: Observing a quantum object isn't gentle: sometimes change is inevitable.
    • Measurement and Memory: Quantum logic means that sometimes probabilities can interfere with one another.
  • Mathematical Foundations: Build up the mathematical formalism for manipulating quantum states by playing with quantum spin.
    • Color Space: The best way to learn vector spaces is through color spaces.
    • Bras and Kets: All the information you'll ever need about a quantum object is contained in a ket.
    • Playing with Basis Sets: There's more than one way to represent a quantum state.
    • Unavoidable Complexity: You can simplify quantum calculations by using vectors, but you can't avoid complex numbers.
    • The Collapse of the State Vector: Sum over all possible histories of a particle by solving Stern-Gerlach puzzles.
    • Operators and Observables: You might better know these quantities as eigenvectors and eigenvalues.
    • Commuting Observables: Sometimes it's impossible to measure two observables at once.
  • Quantum Mechanics: A journey of discovery through the classical underpinnings of Quantum Mechanics, and where they fail.
    • The Photon Catastrophe: Explore the quantum nature of light with some help from Einstein and Compton.
    • Particles and Waves: Maxwell's wave equations are flexible — they can describe light as a wave or a collection of photons.
    • Wide Open Spaces: Learn how to bridge the gap between bras and kets and continuous functions.
    • Squeezing Measurements: There's a limit to how accurately you can measure a particle's position and momentum.
    • Schrödinger's Equation: Derive the one equation to rule them all, and take your first step towards quantum field theory.
    • The Classical Limit: It turns out that Newton's laws were hiding in the Schrodinger equation all along.

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