9 Quantum mechanics
9.1 Introduction: Waves and particles
The first half of the twentieth century witnessed a revolution in physics. Classical
mechanics, with its deterministic world view, was shown not to providea correct de-
scription of nature. New experiments were looking deeper into the microscopic world
than had been hitherto possible, and the results could not be rationalized using clas-
sical concepts. Consequently, a paradigm shift occurred: classical determinism needed
to be overthrown, and a new perspective on the physical world emerged.
One of the earliest breakthroughs concerned the blackbody radiation problem.
The classical theory of electromagnetism predicts that the intensity of electromagnetic
radiation from a blackbody at wavelengthλis proportional to 1/λ^2 , which diverges
asλ→0. Experimentally, the intensity is observed to vanish asλ→0. In 1901, the
German physicist Max Planck postulated that the radiated energy cannot take on any
value but is quantized according to the formulaE=nhν, whereνis the frequency
of the radiation,nis an integer, andhis a constant. With this simple hypothesis,
Planck correctly predicted the shape of the intensity versus wavelength curves and
determined the value ofh. The constanthis now known asPlanck’s constantand has
the value ofh= 6. 6208 × 10 −^34 J·s.
A second breakthrough concerned the so-called photoelectric effect. It is observed
that when light of sufficiently high frequency impinges on a metallic surface, electrons
are ejected from the surface with a residual kinetic energy that depends on the light’s
frequency. According to classical mechanics, the energy carriedby an electromagnetic
wave is proportional to its amplitude, independent of its frequency, which contradicts
the observation. Planck’s hypothesis, however, implies that the impinging light carries
energy proportional to its frequency. Applying Planck’s idea, Albert Einstein was able
to provide a correct explanation of the photoelectric effect in 1905and was awarded
the Nobel prize for this work in 1921. The photoelectric effect also suggests that, in
the context of the experiment, the impinging light behaves less like a wave and more
like a massless “particle” that is able to transfer energy to the electrons.
Finally, a fascinating experiment carried out by Davisson and Germerin 1927 inves-
tigated the interference patterns registered by a photosensitive detector when electrons
impinge on a diffraction grating. This experiment revealed an interference pattern very
similar to that produced when coherent light impinges on a diffraction grating, sug-
gesting that the electrons in such a diffraction experiment behave less like particles and
more like waves. Moreover, where an individual electron strikes thedetector cannot
be predicted. All that can be predicted is theprobabilitythat the electron will strike