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Unformatted text preview: Concepts in Theoretical Physics David Tong Lecture 5: Quantum Mechanics Slogans of Quantum Mechanics s Wave Particle Duality s Discrete “Quantum” Energy s Heisenberg’s Uncertainty Principle s Schrodinger’s Cat s Feynman’s Sum over Histories What is it Good For? s It is the way the universe works at the deepest level. s Technological developments. s Philosophical questions. s New developments in pure mathematics. Atomic Physics Cold Physics s Quantum Mechanics is the way the universe works. But often its effects are washed out unless we look at very small scales s Or very cold temperatures s Much recent progress has been in understanding how quantum mechanics affects macroscopic numbers of atoms Macroscopic Quantum Effects b Superconductivity (discovered 1911, understood 1957) s High Temperature Superconductivity (discovered 1986, still to be understood) b Superfluidity (discovered 1937, understood 1950’s and 1960’s) b BoseEinstein Condensation (understood 1925, discovered 1995) Rotating BoseEinstein Condensates • Quantized rotation: number of vortices = spin 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 The Framework of Quantum Mechanics s Quantum Mechanics is a “framework” rather than a “theory” The Framework of Quantum Mechanics s For example, suppose you’re given Coulomb’s law, describing how electric charges experience a force s You can either choose to think in the classical framework, which means that we plug this into F=ma. s Or you could choose to think in the quantum framework, which means that you plug this into Schrodinger’s equation. s 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 Classical Orbit of an Electron s Consider the electron orbiting the proton. s The classical problem (i.e. F=ma) is exactly the same as a planet orbiting the sun. s The orbits are ellipses, with the sun (or proton) at one focus. s 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. Quantum Orbits of an Electron s In quantum mechanics the answer is very different s The electron can only sit in very particular orbits....
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This note was uploaded on 02/07/2011 for the course PHYS 101 taught by Professor Aster during the Spring '11 term at East Tennessee State University.
 Spring '11
 Aster
 mechanics, Energy, Theoretical Physics

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