Lecture #10 Thurs 21 Feb 2008 Quantum mechanics
Quantum mechanics
Quantum mechanics =
mechanics of very small objects, e.g., atoms.
quantum = packet. Sometimes (not always) the change in a system
is discrete, not continuous.
Like relativity, quantum
mechanics (QM) originates from questions about light and other particles.
Is light really a wave? Is
the electron really a particle?
3 elements:
* photoelectric
effect
* blackbody
radiation and the ultraviolet catastrophe
* electrons
in atoms
The Photoelectric
effect
Last time: Light is a wave but without anything that
“waves.” This turns out not to be the whole story….
1897: J J Thompson
discovers electron at Cavendish
laboratory,
“Crookes tube” = modern
cathode ray tube
“Cathode rays” have a
constant ratio of electric charge to mass
→ they
are particles with fixed (quantized) charge and fixed mass. These are electrons.
1899: shining UV light on
cathode encourages production of electrons = “photoelectric effect.”
1902: Phillip von Lenard
discovers threshhold for photoelectric effect depends on frequency. Intensity
merely determines how many electrons ejected.
Frequency = how many
oscillations per second wavelength ´frequency = velocity = constant for light.
Backbody radiation and
the ultraviolet catastrophe
If you heat up a box
(‘blackbody’) you predict an infinite amount of electromagnetic
radiation inside! (the ‘ultraviolet catastrophe’)
1900: Max Planck shows if
you assume energy in electromagnetic wave is proportional to frequency,
no UV catastrophe.
Electrons in the atom
Electrons live in
matter...but where? J J Thompson: “plum
pudding” model of atom.
1909: at Cavendish Lab,
Ernest Marsden & Hans Geiger (under direction of
Size of atom = one ten
billionth of a meter (= 1 angstrom)
Size of nucleus = 100,000 times smaller ( = 1
fermi)
But opposite charges
attract…why don’t electrons get sucked into the nucleus?
Summary: 3 major puzzles:
* threshhold
of photoelectric effect depends on frequency, not intensity
* Planck’s
energy-frequency relation for blackbody radiation to solve UV catastrophe
* why
does electron “orbit” atomic nucleus?
ANSWER: Everything has
properties of both waves and particles.
1900: Planck “solves”
blackbody radiation by
assuming E = h f .f = frequency, h = Planck’s
constant.
1905: Einstein uses
Planck’s equation to explain photoelectric effect: Electrons trapped by a energy barrier. Light must have a minimum energy (and thus
minimum frequency)
to kick electron out! Einstein awarded Nobel prize 1921 for this. “Light comes in discrete
packets—particles”
1923: Louis de Broglie:
Maybe electrons (particles) act like waves! This explains atoms
Must fit
a complete number of wavelengths in orbit around atom, otherwise “not allowed.”
Modern quantum
mechanics
1925-26 complete quantum
theory developed by Schrodinger, Heisenberg, Born, Bohr:
Classical mechanics: each
particle has a trajectory computed from forces and
Quantum mechanics (QM):
each particle has a wavefunction Ψ(x,t).
The wavefunction Ψ(x,t) changes with time according to Schrodinger’s equation:
Classical mechanics: x(t) tells you position of particle at time t
QM: | Ψ(x,t) |2 is the probability
to find the particle at time t and at position x.
1927: Davisson and Germer
experiment shows electrons are waves (diffraction and interference).
QM is a probabilistic
theory. You cannot predict the outcome of
any single measurement. But you can predict probabilities for many
measurements.
Einstein did not like
this.
There are many
“interpretations” of the same math for QM.
Most physicists use the “
One alternate
interpretation (of many): Everett-Wheeler many-worlds interpretation: there are
infinite universes and in each one the atom is measured at a different place.
Quantum mechanics in SF
QM generally misused in SF
(worse than relativity). QM used to justify faster-than-light jumps or
faster-than-light communication via entanglement (won’t really work).
Also: many-world
interpretation used to justify parallel universes (better, but still not
accurate)
Both Timescape and The
Dispossessed argue against the
probability (random) nature
of quantum mechanics.
Quantum mechanics
summary
The mechanics of very
small objects
size of atom = 10-10 meters ( = 1 Angstrom)
size of atomic nucleus = 10-15 m (= 1 fermi)
Basic results:
waves (like light) can act as particles
-- photoelectric effect
-- no “ultraviolet catastrophe”
for blackbody radiation
particles (like electrons) can act as waves
-- fixed (“quantized”) orbits for electrons around atoms
-- Davisson-Germer showed electrons have diffraction (interference)
Objects (light, electrons)
described by wave function
The wavefunction predicts
the probability of any outcome, not the specific outcome itself
Many-worlds
interpretation: at each quantum event universe splits into separate universes