Lecture #10 Tues 2 Mar 2010 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, Cambridge.

“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 Rutherford) discover atom has massive, tiny nucleus… “Planetary model.”

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 Newton’s laws.

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 “Copenhagen interpretation” developed by Niels Bohr: after experimenter observes/measures the (say) atom, the wavefunction collapses because probability to be elsewhere is zero.

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 Copenhagen interpretation: wavefunction “collapses” upon making a measurement / observation

Many-worlds interpretation: at each quantum event universe splits into separate universes