Heisenberg’s Uncertainty Principle

Uncertainty Principle put forth by W.Heisenberg in 1928. This has no classical analogue but is one of the basic concepts in quantum mechanics. If we have a source of monochromatic light (single wavelength) at the back of two slits we would obtain a diffraction pattern i.e. bands of dark and light areas. Dark bands correspond to the regions where light does not strike and light areas correspond to areas where light is able to reach. Replace now the source of light with source of mono energetic electrons from an electron gun. We would be able to see an interference pattern similar to that with light.

We would get the diffraction pattern of light and dark regions by exposure of photographic plate to electrons. For much reduced intensity we would see blurred interference pattern and with further reduction of electron beam intensity we may get only a couple of spots and no bands of light and dark areas. However electrons appear to have gone to places where intensity maxima appear in diffraction pattern.

This is perhaps hard to accept as we think of any particle or body having precise location at a precise time. This means that it would appear at one of the slits at a given time (classical mechanics concept). Can we now think of an experiment to determine through which slit the electrons go to produce diffraction pattern? For this, we can perform an experiment in which we shine the slits with light. Suppose we illuminate the slits with X-rays of short wavelength for accurate measurement. By measuring the scattered radiation we should know through which slit the electrons passed. This would give us a result showing that 50 % electrons went through one slit and 50 % through the other.

However we would see that there is no interference or diffraction pattern produced at all. Our new experiment has destroyed the interference pattern. This is because, as we know, due to Compton effect electron changes its energy and direction. Without X-rays striking the electrons, they went to produce interference pattern or there were only certain momenta allowed for the electrons. After Compton scattering the electrons got other momenta from the photons so that they could reach the previously forbidden regions. On the other hand we can use very long wavelength. Location of electron can be determined with a precision of oe/2.

If wavelength is very large, precision would be lost and we would not know through which slit the electron came out. In other words we cannot precisely know position and momentum of the electron simultaneously with arbitrary accuracy. If we reduce the momentum uncertainty (using long wavelength), position becomes uncertain and if we measure the position with certainty using short wavelength then momentum becomes uncertain destroying the diffraction pattern.

Indeed it is not possible to keep both position and momentum measurement precise, simultaneously. Precise measurement of one disturbs the other measurement. This is known as Heisenberg’s uncertainty principle, It is expressed as

(del.x).(del.p) >= h/2(pie)