Actually, tk421, you might have made that observation about virtually all responses to the OP.

Shame on you all!

Let's see......

First notice in QM, the wave function

is considered as an element in an Hilbert space of square integrable functions.

As such it is a vector, and QMers write

for this guy.

Now as a vector, it is entitled to be operated on by - doh - an operator, in this case it is called a Hamiltonian operator

.

Now any operator acting on a vector is in turn entitled to an eigenvalue - in this case a Real number. One writes

where

is set of Real number - eigenvalues for this operator - called the spectrum of the operator, which may be discrete (have "gaps" between elements) or continuous (otherwise)

Now the operator

is by definition the sum of a kenetic energy term

and a potential energy term

, say (this is not standard notation!) - these are both operators in their own right.

It was first suggested by Count Louis de Broglie in the 1920' that to any subatomic particle, even one with mass one can associate a wave fnction (though he didn't say how!)

Now we know we can always relate kinetic energy of a massive particle to momentum by

Likewise we now that potential energy

has something to do with position - just as it has in a gravitational field (though of course no gravity is acting here).

So, assuming that knowledge of either

or

has no effect on the spectrum of

, we may say that

knowing

exactly by measurement, means that

may be almost anything, and likewise the other way around.

Now notice that, as a function

maps any Real number to the interval

- that's what it means to be a wave function

It was Max Born (I believe) who suggested that the absolute square of the range of

(i.e.

) could be interpreted as the probability of a certain eigenvalue for

for position with fixed momentum, and likewise for momentum with fixed position.

Does this mean a subatomic particle can ne in 2 places at once?

You tell me!!