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Quantum Mechanics from the Tombs Peter Leung Feb. 16, 2011

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Pre-20 th Century Specific heat of diatomic gases: Discrete spectra: Angstrom (~ 1860)

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Max Planck ( )

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Planck: The Quantum Revolution Planck U October 19, 1900 December 14, 1900 E = N ε = N h f Ref.: Thomas Kuhn:“Black-Body Theory and the Quantum Discontinuity, ”

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How did Planck discover the “quantum”? To calculate cavity radiation intensity, need the energy density ~ U(T) Now we have and To calculate W, need to assume Then use combinatorics => W:

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Planck’s tomb

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Niels Bohr ( ) The “Godfather” of Quantum Mechanics “If you are not shocked by quantum mechanics, you have not understood it!”

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Quantum Structure of Matter (1913) m v r = n h /(2π) ( h has a dimension of angular momentum!) Derivation of Rydberg constant: R = x 10E7 /m

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Other significant contributions Correspondence Principle (1918): h → 0 or n →∞ : Quantum → Classical Principle of Complementarity (1928): Two contradictory pictures (wave/particle) of reality complement each other Copenhagen Interpretation of QM (1928)

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Here lies Niels Bohr - now in the ground state. --- John Hubisz

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Prince Louis-Victor de Broglie ( )

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Discovery of matter wave Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis Paris, (Advisor : Paul Langevin) Einstein’s endorsement (any impact on the Bose-Einstein condensation?) For light: E = hf p = E/c = hf/c = h/λ Radiation-matter equivalence: E = mc^2 → For matter: f = E/h λ = h/p

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Werner Heisenberg ( )

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Discovery of Matrix Mechanics Professors: Sommerfeld, Wien Main ideas: theory should only contain observable (measurable) quantities -- frequency of electron in atom : ω → ω(mn) -- position of electron in atom : x → x(mn) -- momentum of electron in atom : p→ p(mn) → noncommuting x, p: x p – p x = ih /2 0

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Uncertainty principle (1927) Heisenberg: thought experiment with gamma ray microscope (qualitative statement: x p h ) Kennard (1927): x p h/4 Robertion (1929): x p /2i

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Epitaph for Heisenberg He lies here, somewhere.

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Erwin Schrodinger ( )

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A Christmas Romance (1925) From Leon Lederman: “The God Particle” “Matter Waves and the Lady in the Villa” … Leaving his wife at home, Schrodinger booked a villa in the Swiss Alps… taking with him his notebooks,… and an old Viennese girlfriend …Then he placed the girlfriend in bed for inspiration…

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The Celebrated Equation (1926) For Light: wave equation → ray (eikonal) equation as wavelength → 0 For matter (e.g. an electron): particle (“ray) equation: F = ma →

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Entanglement (1935) The poor pet…

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Epitaph by John Hubisz Here lies Erwin Schrodinger - but without opening the casket, we can't be sure he's dead.

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His Later Regrets… Erwin Schrodinger : If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory.... never like duality, probability,… till the end

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Max Born ( )

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Formulation of Quantum Mechanics First published using the term: “Quantum Mechanics” --- (1924) Completed matrix mechanics with Heisenberg and Jordan (1926): Engraving:

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Tomb Inscription

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Probability: an indeterministic universe from a foot note! Study of scattering problem: switch to wave mechanics (1926)

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Paul Dirac ( ) Bohr: ‘ Of all Physicists, Dirac has the purest soul…’ (Graham Farmelo: “The Strangest Man”)

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Discovery of the “Quantum Possion Bracket” (1925) Heisenberg → Fowler → Dirac Classical Possion Bracket Quantum commutator

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The Dirac Equation (1928) Relativistic wave equation for the electron: spin and antiparticle Westminster Plaque

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Other Contributions Dirac delta function (1927) Transformation theory (1927) Theory of holes (1930) Magnetic monopoles (1931) Lagrangian in quantum mechanics (1932) Large number hypothesis (1938) Bra and ket (1939)

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Other Significant Contributors Einstein Pauli Jordan Eckart Von Neumann Feynman Bell

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More References

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One of the Latest (and very good one!)

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