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

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

Max Planck ( )

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, ”

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:

Planck’s tomb

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

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

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)

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

Prince Louis-Victor de Broglie ( )

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

Werner Heisenberg ( )

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

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

Epitaph for Heisenberg He lies here, somewhere.

Erwin Schrodinger ( )

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…

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 →

Entanglement (1935) The poor pet…

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

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

Max Born ( )

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

Tomb Inscription

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

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

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

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

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)

Other Significant Contributors Einstein Pauli Jordan Eckart Von Neumann Feynman Bell

More References

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