"Greg Egan - Foundations 4 - Quantum Mechanics" - читать интересную книгу автора (Egan Greg)

ignored, but it was not at all clear how to synthesise the two into a coherent new
description of electromagnetism.
In parallel with these revelations about light, physicists were grappling with the
problem of the structure of atoms. Electrons had been discovered in 1897, and in 1911
Ernest Rutherford had found strong experimental evidence for the theory, first proposed
by Hantaro Nagaoka, that atoms consisted of electrons orbiting a positively charged
nucleus. The puzzle here was that charged particles moving in a circle emit
electromagnetic waves, so the electron should have radiated away all its energy and
plunged into the nucleus. Not even Planck's quantised photons could rule this out.
In 1913, Neils Bohr proposed that the energy of the electrons themselves was
quantised, and the existence of a minimum allowed energy kept them from falling into the
nucleus. Bohr came up with a formula for the energy levels of the single electron in a
hydrogen atom, constructed in order to agree with the observed spectrum of light emitted
and absorbed by hydrogen. This spectrum consisted of a discrete set of sharply defined
 Egan: "Foundations 4"/p.6


frequencies, which could now be interpreted as the frequencies of photons whose
energies matched the differences in energy between the allowed states of the electron.
An electron could only move to a higher energy level by absorbing a photon that provided
exactly the right amount of energy, and it could only drop back to a lower level by
emitting a photon that carried the energy away again. This was by far the most
successful model of atomic structure to date, but Bohr's formula was even more
mysterious than Planck's. Why were only certain energy levels available to the electron?
The first hint at an answer came from the suggestion by Louis de Broglie in 1924
that matter, as well as radiation, might behave like both a wave and a particle. This was
confirmed spectacularly a few years later, in experiments showing that electrons fired at a
crystal were reflected back most often in certain directions: those in which a wave that
scattered off the regularly spaced atoms of the crystal would undergo constructive
interference. Since then, interference effects have been demonstrated for all kinds of
particles, including entire atoms.
To examine de Broglie's idea more closely, we need to ask what the wavelength
and frequency of the тАЬmatter waveтАЭ associated with a particle should be. One reasonable
starting point is the relationship that worked so successfully for Planck with photons:
E=h F. Since F is the frequency of the wave (the number of oscillations per second), the
period of the wave, the time each oscillation takes, is:


T = 1/F
= h/E (2)


Since the wave for a photon is moving forward through space at the speed of light, c,
each cycle is spread out over one wavelength:


L = cT
= c h/E