Chapter 4 Further developments
The hectic period of fundamental quantum discovery in the mid1920s was followed by a long developmental period in which the implications of the new theory were explored and exploited. We must now take note of some of the insights provided by these further developments.
Tunnelling Uncertainty relations of the Heisenberg type do not only apply to positions and momenta. They also apply to time and energy. Although energy is, broadly speaking, a conserved quantity in quantum theory – just as it is in classical theory – this is only so up to the point of the relevant uncertainty. In other words, there is the possibility in quantum mechanics of ‘borrowing’ some extra energy, provided it is paid back with appropriate promptness. This somewhat picturesque form of argument (which can be made more precise, and more convincing, by detailed calculations) enables some things to happen quantum mechanically that would be energetically forbidden in classical physics. The earliest example of a process of this kind to be recognized related to the possibility of tunnelling through a potential barrier. The prototypical situation is sketched in figure 7, where the square ‘hill’ represents a region, entry into which requires the 58
