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  The concept of quantization, in physics, is difficult to assimilate, since it only occurs on a very small scale, and thus we have no direct experience of it. In essence, it means that certain basic quantities, like energy and angular momentum, may only have certain values. The first ideas about quantization come from ancient Greece. The Greeks reasoned that a substance cannot be divided into smaller parts indefinitely: the smallest possible part of the substance will be reached, which cannot be further divided and still retain its nature. The ancient Greeks named these indivisible objects atoms (‘uncuttable elements’). The word was taken up by early chemists who discovered their existence.

In modern physics, quantization has a slightly different meaning. Energy itself is not quantized, but a system like an atom may only accept or emit quanta of energy. The atom can only exist with certain definite amounts of energy, and not with any energy in between these levels.

The basis of quantization is the wave nature of matter. If we accept that all particles have a wave-like nature, then it may be seen that this nature imposes quantization upon them. An example of how waves imply quantization is to be found in the behaviour of a vibrating string.

A string fixed at both ends has only certain modes of vibration. The easiest of these to excite has its maximum amplitude of vibration in the centre, with no movements at the ends. The next mode of vibration has a still point at the centre (a node) and a maximum amplitude of vibration (antinode) at points one quarter and three quarters of the way along. The next mode will have two nodes and so on.

What may be noticed is that any modes of vibration that do not have nodes and antinodes in exactly the right place do not exist upon the string: they are not allowed. We can see that they would not be very successful; a mode with an antinode at a fixed end will not get very far! As the energy of a vibrating string depends upon its mode, the allowed energies of the string are quantized.

A particle confined within a certain area (like an electron orbiting an atom) is now considered to be strongly analogous to a wave on a string fixed at both ends. Thus its allowed energies are not continuous but only occur at certain values. This is found to be true in experiments; atoms only have certain energy levels.

Energy is not the only quantity that is quantized in confined systems. Other quantized quantities are velocity, angular momentum and magnetic moments. JJ



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