Quantum Mechanics ¯h = 1.0545716 10 kg m sec

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— All science is either physics or stamp collecting.
Ernest Rutherford, 1st Baron Rutherford of Nelson
(Nobel Prize for Chemistry, 1908)
0.1 Quantum mechanics past, leading to present
Quantum mechanics 1 is a way of thinking, and talking, about the world that
leads to so radical a departure with what is considered classical, or ‘everyday’
physics, that some of its consequences appear outrageous 2 . Nevertheless, as
far as we can see it is a more correct way 3 , and the classical world pictures of
Newton and Maxwell are seen to be only approximations — albeit often very
excellent ones.
The historical roots of the development of quantum mechanics, around the
turn of the 20 th century, are diverse and have been fed by dissatisfaction with the
performance of classical physics in the description of a number of phenomena.
The most important of these are the behaviour of black-body radiation, that led
Max Planck to introduce his famous Planck’s constant ; the unexplained but
undeniable stability of atoms that motivated Niels Bohr to invent quantization
rules ; the photo-electric effect that induced Albert Einstein to postulate that
light waves are actually composed of particles, the photons ; and on top of
that the complementary idea of Louis de Broglie 4 that, by symmetry, particles
might as well be thought of as waves. Of these, black-body radiation is too
difficult, and photons are both too simple and too relativistic, to be discussed
in a very elementary text as this ; the quantum-mechanical hydrogen atom will
be discussed in some detail in following courses ; the particle-wave duality will
be treated in these lectures. The primordial (but unaware) founding father of
quantum mechanics is Josiah Willard Gibbs 5 who, in studying the Gibbs paradox
about the entropy of gas mixtures, gave the world the notion that a finite list
of properties can be enough to specify a system completely 6 , by introducing the
notion of indistinguishable particles 7 .
A chronological description of quantum mechanics, following its historical
development, makes for entertaining and instructive reading, but from the point
of view of equipping physics students with what they need to know it makes as
much sense as teaching people to read and write by first explaining to them
cuneiform and hieroglyphs, Phœnician and Greeks alphabets, majuscules and
1 We shall restrict ourselves to nonrelativistic quantum mechanics in these notes.
2 Such as the consequences of the work of John Bell, which allow us to propose that reality
may not have any properties of itself.
3 In the sense that, where classical and quantum predictions differ, quantum always turns
out to be right — so far.
4 In full : Louis-Victor-Pierre-Raymond, 7me duc de Broglie.
5 Less universally famous than he would deserve to be, not least for his statement that “A
mathematician may say anything he pleases, but a physicist must be at least partially sane”.
6 Look up any textbook on statistical physics on this.
7 Which we nowadays know as fermions and bosons.
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