
Quantum Theory 

1.1 Quantisation of energy
Quantum theory was initially formulated in 1900 by the
German physicist Max
Planck in response to the problem of the radiation emitted by
a ‘blackbody’ (so called because it absorbs all radiation
that falls upon it; it is also a perfect emitter). The combination of the two hypotheses implied that the discrete frequencies
found in atomic line spectra implies that the atom, as a quantum body,
has certain, discrete ‘energy levels’, and can only absorb
or emit energy in certain, discrete amounts, which are multiples of hn.
Bohr was also awarded the Nobel Prize in Physics, 1922, for this work. 1.2 Special relativity and waveparticle duality Later, in 1923, de
Broglie suggested that electrons (and photons, themselves also being
particles) might have a wave property associated with them, as a result
of applying Einstein’s special relativity, E
= mc^{2}.[4]
…where p is the linear momentum. The
equation also holds for a photon travelling at the speed of light, c.
The photon differs from the electron in that it always travels at speed
c and has zero rest mass (but can have appreciable
relativistic mass), whereas the electron has a speed less than c
and a nonzero rest mass. 1.3 The uncertainty principleThe uncertainty principle was discovered in 1927 by Werner Heisenberg.[6] It states that, as a consequence of the waveparticle duality of microscopic ‘particles’, there is a limit as to how accurately the position and momentum of such particles can be simultaneously defined. It is typically represented mathematically in the form shown in equation (1.3):
The uncertainty principle can be demonstrated experimentally by the attempt to measure simultaneously the x coordinate and the x component of linear momentum, of a microscopic particle, as a beam of such particles is passed through a diffraction grating or slit (see Levine[7]). 1.4 Further information and indeterminacyThe wave nature of a particle can be demonstrated by a simple twoslit
diffraction experiment  an explanation of this is given at the Physics
Department at Trinity College, Dublin's minisite about quantum theory,
which you can find here.
There are also some great interactive applets at the University of Colorado's
“Physics 2000” site (in the Interference
Experiments section of the Atomic Lab) which illustrate these effects.
The 'electron gun' applet, illustrating twoslit diffraction of particles
is linked here for convenience:
For a given spot on the phosphor screen, we cannot know which slit the wave/particle that caused it has come from. This is indeterminacy, and is a fundamental consideration in the difference between macroscopic and quantum ideas. It is often conceptualised using the famous Schrödinger's cat ‘thought experiment’. 

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[1] M. Planck, “Über das Gesetz der Energieverteilung im Normalspektrum”, Ann. d. Physik, 4, 553, 1901 [2] A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Ann. d. Physik, 17, 132, 1905 [3] N. Bohr, Fysisk Tidsskrift, 12, 97, 1914 [4] L. de Broglie, Comptes rendus de l'Académie des Sciences, 177, 507510, 1923 [5] HyperPhysics, Wave nature of the electron: http://hyperphysics.phyastr.gsu.edu/hbase/davger.html#c1 [6] W. Heisenberg, Z. Physik, 45, 172, 1927 [7] Ira N. Levine, “Quantum Chemistry”, 5th edition, PrenticeHall International (UK) Limited, 2000 
Potential Energy Surfaces and Conical Intersections • June 2002 • Ian Grant 