Heisenberg Uncertainty Principle

Have you ever heard of the Heisenberg uncertainty principle? I was told about it when I was studying A-Level Chemistry, it basically states that the more you know about the momentum of a particle the less you know about the position and vice versa.

Why should that be? Doesn't that strike you as strange? The very act of determining a particle's position means that you cannot know it's velocity.

 One experiment introduced by Heisenberg, which helps clarify this idea is; to see an electron, and thus determine it's position, you might use a powerful light microscope. For the electron to be visible, at least one photon of light must bounce off of it, and then pass through the microscope into your eye. A problem occurs here, as the photon transfers some unknown amount of its momentum to the electron. Thus, in the process of finding an accurately position of the electron, the same light that allows you to see it changes the electron's momentum to an undeterminable extent.
 Another way of looking at this is by considering wavefunctions. If you know the exact wavelength of a particle, then you know it's momentum. However a particle with a known momentum has a totally unpredictable location. You can see this if you look at the graph left - the electron is equally likely to be anywhere along the wave.

The wave function of a perfectly localised particle would be a sharply spiked function at the particles position and zero everywhere else. This can be aproximated by the addition of of several waves, which interfere constructively in one place and destructively in all others. However in doing this you loose information about the momentum of the particle - there is no well defined wavelength.

 As more waves are used in the supposition (given by numbers on curves) the location becomes more precise at the expense of uncertainty in the particles momentum An infinite number of waves is needed to construct the wavefunction of a perfectly localised particle - so there is total uncertainty in the momentum

Important things to note:

• Due tothe small value of h in everyday units, this principle is only significant on the atomic scale.

• The uncertainties of Dx and Dp arise from the quantum structure of matter, and are not due to imperfections in the measurement instruments.

graphs taken from: Physical Chemistry, Peter Atkins, 6th Ed, OUP (1998)