6. Development of QM
Ideal gas
Equipartition all molecules eventually end
up in distribution around same kinetic energy
“Gas” of radiant energy
“UV catastrophe”
8. Max Planck
Postulated quantization of
energy in 1900
Radiant energy only comes in
packets of size hν
With this restriction, you get
the observed distribution!
10. Development of QM
Bohr, 1911: quantize energy of electrons, too
kicked out of Thomson’s group, joins
Rutherford, who has discovered nucleus
Nucleus + orbiting electrons + classical EM
radiation atom lifetime of ~10-8 seconds
12. Development of QM
de Broglie waves, 1925
Pauli exclusion principle, 1925
Goudsmit and Uhlenbeck, spin, 1925
13. Development of QM
Schrödinger, 1926: wave mechanics
Heisenberg, 1926: matrix mechanics
Give same results, but conceptually very
different
In 1927 Schrödinger proved they are
identical!
15. Uncertainty for bullets
ΔpΔq ≃ h = 6.6 x 10-34 J s = 6.6 x 10-34 kg m2 s-1
Mass of bullet is about 0.010kg, so for bullet ΔvΔq ≃
6.6 x 10-32 m2 s-1
Muzzle velocity of bullet is about 1000 m s-1 (~2200
miles per hour), so if we know the bullet velocity to a
part in 1012 (~±1mm per century!), Δv = 10-9 m s-1
Δq ≃ 6.6 x 10-23 m
Atomic nucleus is ~10-15 m across, so uncertainty is
insignificant for macro-sized objects
16. Uncertainty for atoms
Mass of electron is 10-30 kg
Thus ΔvΔq ≃ 6.6 x 10-4 m2 s-1
For electron confined in atom of size Δq ≃ 10-10 m,
Δv ≃ 6.6 x 106 m s-1
This gives ΔKE of ~ 10 eV, or on the order of the
electron’s binding energy!
Orbits along lines are nonsensical — don’t know
where electron is going next
17. Complementarity
An object has both wave and particle
properties, but both cannot be observed at
the same time
Double slit experiment — Heisenberg’s
“Swerve left? Swerve right? Or think about
it and die? In your head you swerve both
ways...”
19. History
Bohr, Fermi in Washington in 1939 at conference
News came to Bohr by telegram of Frisch and
Meitner’s discovery of fission by fast neutrons
Gamow says implications discussed and
understood by all at conference
Einstein writes to Roosevelt, 1939
Manhattan Project, Robert Oppenheimer, 1941-45
20. History
Results of Manhattan Project — enough 235U to build a bomb,
Trinity test in NM, Hiroshima, Nagasaki
Germans working on Pu bomb, heavy water moderated reactor
for Pu production
German team captured, held at Farm Hall in England, recorded
— they heard of Hiroshima while in captivity
Heisenberg describes Hiroshima bomb, 235U critical mass to
Gerlach, apparently for first time
Farm Hall transcripts support the “we didn’t want to succeed”
version, but they are after the fact and after the horror of
Hiroshima
21. History
Bohr’s 11 draft letters
to Heisenberg, 1957-62,
released in 2002 (after
Copenhagen written)
Bohr says Heisenberg
sure of German victory,
and that if the war
lasted long enough it
would be decided by
nuclear weapons
22. History
Heisenberg took many trips for Cultural
Division of German Foreign Service, not just
to visit Bohr
Told Dutch colleagues in 1943 that either
Germany or Russia would dominate Europe,
and Germany would be better for them
23. German project failed — why?
Heisenberg sabotaged it?
Heisenberg was only a theorist, and could not do the
mammoth engineering required?
Heisenberg was too cocky, and didn’t do the
calculations?
Germany pursued jets and rockets instead?
Heisenberg used fission as a means to a prestige
appointment, then moved back to doing basic physics?
25. Copenhagen, Michael Frayn, with Postscript, 1998
Thirty Years That Shook Physics, George Gamow, 1966
The Making of the Atomic Bomb, Richard Rhodes, 1987
The Feynman Lectures on Physics, 3 volumes, Richard
Feynman, 1965
“Werner Heisenberg and the Uncertainty Principle”,
http://www.aip.org/history/heisenberg
Bohr’s draft letters, http://nba.nbi.dk/papers/
introduction.htm
Notes de l'éditeur
Bohr godfather of quantum mechanics, Bohr model of atom, leader of group that developed quantum mechanics. “Copenhagen interpretation” because it was developed at his Institute in Copenhagen, from approximately 1924-27.
Heisenberg known as very fast thinker and worker--almost too fast for his own good. Story in play of Heisenberg doing uncertainty while Bohr skiing in Norway and submitting the paper before Bohr returned—Bohr very upset.
Bohr known as slow and plodding, but got through to every implication of the work. Famous for innumerable drafts of his papers, all typed by Margrethe. Bohr kidded in play about how slowly he skis, and about drafts.