So you often see this explained by the apparent fact that as soon as you make a measurement on an elementary particle then you of necessity alter its state. This is fine as far as it goes, but it is as well to remember this is a mere analogy (I believe it was suggested to Heisenberg by Pauli, though I am not completely sure)

However there are some problems here: ask a modern physicist and she will probably say something like "a quantum entity is neither a wave nor a particle but, depending on how you measure it could show some properties of either one or the other or both simultaneously"

Let us take a more simplistic view, one that both de Broglie and Schroedinger took.: to every elementary particle one can associate a wave function .

Now it is a fact that the playground of Quantum Mechanics is an Hilbert space of square-integrable functions called "state vectors", so let us assume that our wave function is one such. To celebrate, let's write this as . As this is a vector, it is entitled to be acted upon by some operator, so let us, following Schroedinger choose the Hamiltonian with the property that

Never mind what actually is, just note that the is called an "energy eigenvalue" associated to this operator.

Let us now consider what our wave function/state vector is. It is a function that takes on values in with period where n is integer.

OK, so forget the "eigen" bit, and assume that to any particle, via its associated wave functions, there may be many possible energies, anda priorwe have no way of knowing which wave function/energy to assign to it. But the process of measuring energy is just to select a single wave function.

Here's the crucial point: it was first pointed out by Max Born (I think) that one may interpret the square of the wave function as a position probability density for our particle. So that having measured its energy, and thereby selected a PARTICULAR wave, all we can say about its position is in terms of this probability density.

Conversely, assume we know exactly where our particle is. Then our probability density will be unity at some point, and zero everywhere else. The only way to obtain such a wave with the properties I describe is to "muddle together" (physicists call this superposition) a large number of different waves that interfere destructively at all points except one, where interference is constructive and square all of these.

In other words, if you know the position, you are faced with a multiplicity of possible energies, and no way to decide between them