Transcript The Revolution and Evolution of Quantum Mechanics

Quantum Mechanics from the
Tombs
Peter Leung
Feb. 16, 2011
Pre-20th Century
• Specific heat of diatomic gases:
CV  3 R  2 R  5 R : no contribution from vibrational motion
2
2
2
unless at very high temperatures
• Discrete spectra:
Angstrom (~ 1860)
Max Planck (1858-1947)
Planck: The Quantum Revolution
• Planck
U
October 19, 1900
C1 f 3
U ( f , T )  C2 f /T
e
1
December 14, 1900
E=Nε=Nhf
Ref.: Thomas Kuhn:“Black-Body Theory and the Quantum
Discontinuity, 1894-1912 ”
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:
N  nU
Planck’s tomb
Niels Bohr (1885-1962)
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 = 1.0973731 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
(1892-1987)
Discovery of matter wave
• Recherches sur la théorie des quanta
(Researches on the quantum theory), Thesis
Paris, 1924. (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 (1901-1976)
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  <[x,p]>/2i
Epitaph for Heisenberg
He lies here, somewhere.
Erwin Schrodinger (1887-1961)
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 →
H  i

t
Entanglement (1935)
• The poor pet…
 (1, 2)   (1)   (2)
1  cat
2 = decaying atom
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 (1882-1970)
Formulation of Quantum Mechanics
• First published using the term: “Quantum
Mechanics” --- (1924)
• Completed matrix mechanics with Heisenberg
and Jordan (1926):  x, p   i 
ij
• Engraving:
ij
Tomb Inscription
Probability: an indeterministic
universe from a foot note!
• Study of scattering problem: switch to wave
mechanics (1926)
........................ . . . . . . . . .
Paul Dirac (1902-1984)
• Bohr: ‘ Of all Physicists, Dirac has the purest
soul…’ (Graham Farmelo: “The Strangest Man”)
Discovery of the “Quantum Possion
Bracket” (1925)
• Heisenberg → Fowler → Dirac
 x, p  xp  px  i
Classical Possion Bracket
x, p =1
0
Quantum commutator


1
i
1
 x, p =1
i
The Dirac Equation (1928)
• Relativistic wave equation for the electron:
spin
and
antiparticle
 c p   mc 2  V   i
Westminster
Plaque

t
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
•
•
•
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Einstein
Pauli
Jordan
Eckart
Von Neumann
Feynman
Bell
More References
One of the Latest (and very good one!)