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Concepts In Theoretical Physics - Quantum Mechanics

Concepts In Theoretical Physics - Quantum Mechanics -...

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Concepts in Theoretical Physics David Tong Lecture 5: Quantum Mechanics
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Slogans of Quantum Mechanics square6 Wave Particle Duality square6 Discrete “Quantum” Energy square6 Heisenberg’s Uncertainty Principle square6 Schrodinger’s Cat square6 Feynman’s Sum over Histories
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What is it Good For? square6 It is the way the universe works at the deepest level. square6 Technological developments. square6 Philosophical questions. square6 New developments in pure mathematics.
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Atomic Physics
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Cold Physics square6 Quantum Mechanics is the way the universe works. But often its effects are washed out unless we look at very small scales square6 Or very cold temperatures square6 Much recent progress has been in understanding how quantum mechanics affects macroscopic numbers of atoms
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Macroscopic Quantum Effects boxshadowdwn Superconductivity (discovered 1911, understood 1957) square6 High Temperature Superconductivity (discovered 1986, still to be understood) boxshadowdwn Superfluidity (discovered 1937, understood 1950’s and 1960’s) boxshadowdwn Bose-Einstein Condensation (understood 1925, discovered 1995)
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Rotating Bose-Einstein Condensates • Quantized rotation: number of vortices = spin
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Dividing the Indivisible • Electrons are elementary particles. They have no constituent parts • Yet we frequently perform experiments where they split up! • This is an article from 2 weeks ago
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The Framework of Quantum Mechanics square6 Quantum Mechanics is a “framework” rather than a “theory”
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The Framework of Quantum Mechanics square6 For example, suppose you’re given Coulomb’s law, describing how electric charges experience a force square6 You can either choose to think in the classical framework, which means that we plug this into F=ma. square6 Or you could choose to think in the quantum framework, which means that you plug this into Schrodinger’s equation. square6 It’s like running a programme on different operating systems...and the operating system of the universe is quantum mechanics F = Q 1 Q 2 4 πr 2
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Classical Orbit of an Electron square6 Consider the electron orbiting the proton. square6 The classical problem (i.e. F=ma) is exactly the same as a planet orbiting the sun. square6 The orbits are ellipses, with the sun (or proton) at one focus. square6 But there’s no restriction on the size or eccentricity of the orbit….that depends only on initial conditions of the problem The question of the distances between the planets used to be the biggest open problem in science. But we now know that it’s a complicated question that isn’t answered by the fundamental theory.
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Quantum Orbits of an Electron square6 In quantum mechanics the answer is very different square6 The electron can only sit in very particular orbits.
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