Why doesn't the electron have a definite position?

[mahela007]

I have understood that an electron can be thought of both as a wave and as a particle. But I still don't understand why we can't give it a definite position...

 

[RedX]

Well if we gave it a definite position, then it wouldn't really be a wave?

 

[fatra2]

Hi there,

Try to imagine (classically) the speed of an electron around a nucleus. Now to find out precisely the position of the electron, you would need to know so many different parameters at the same time, that it becomes physically impossible to do so.

From the Heisenberg uncertainty,\Delta x \times \Delta p \geq \frac{h}{2} fixes the precision of the position. If you decide to be super-duper precise on the position, then you have absolutely no-more clue about it speed. Therefore, you will not be able to keep track for very long of the "exact" position.

Cheers

 

[VincentJL]

Actually, in the QM description electrons can in fact have a definite position, however only when they are in such a state that the energy is completely undefined.

As fatra2 states, it has to do with the Heisenberg uncertainty.

Without diving into the math, you could say that it is simply a result of the formulation of QM, which leads to the question of "How fast was the electron going when it was at x" becoming utter nonsense. It's kinda like the joke
"If it takes two men two hours to dig a hole, then how long would it take one man to dig half a hole?"
Per definition, there is no such thing as half a hole, therefore the question makes no sense. Similarly in QM where you describe an electron with a wavefunction, there is no such thing as a simultaneous position and velocity (or energy).

 

[ytuab]

I have understood that an electron can be thought of both as a wave and as a particle. But I still don't understand why we can't give it a definite position...

Unless we make new theory replacing the Schrödinger equation, all we can do is only believing the uncertainty principle. (even if the uncertainty principle seems strange to us.)

Some people may dream of treating the electrons as real particles based on the Schrödinger equation, but these methods won't work.

If we try to treat the electrons as real particles (with definite momentum and position),
we must forget the idea of the Schrödinger equation.

At first Schrödinger thought that the electron is wave (and a particle).
But the wave packets will be spreading in all space with time (this means the electron will become bigger and bigger with time.)
So, later he changed his idea, and he thought the wave(function) means the probability density
of the electron.

 

[Count Iblis]

Also, from to the uncertainty relation it follows that trying to locate an electron to within a region the size of the Compton wavelength would require measurements at such high energies that electron-positron pairs would be created. Then, there is no way to know which electron's position you need to measure, as all electrons are exactly identical.

 

[mahela007]

Thanks for the replies... they all helped.
So let me sum up to see if I got it right.
The electron is buzzing around and we have no way of predicting where it will be because of a fundamental law of nature (the uncertainty principle). The electron can be at any place given by it's wave function... (right?)

One final question:
Although we can't exactly "find" the electron, does it have a position in space? Logically, it seems that it should. (my logic has been known to be faulty.)

 

[vociferous]

Thanks for the replies... they all helped.
So let me sum up to see if I got it right.
The electron is buzzing around and we have no way of predicting where it will be because of a fundamental law of nature (the uncertainty principle). The electron can be at any place given by it's wave function... (right?)

One final question:
Although we can't exactly "find" the electron, does it have a position in space? Logically, it seems that it should. (my logic has been known to be faulty.)

I think it is more along the lines of this:

We do have a way of "predicting where it will be"; there is a probability wave, which tells us the likelihood of finding it in a specific "location", but it does not actually occupy that "location" until we measure the position (collapsing the probability wave). The more precisely one measures the position, the less one knows about the momentum.

In fact, it is important to keep in mind that electrons have discreet energy levels, which is especially relevant when they are bound to an orbital around a nucleus.

 

[mahela007]

I think it is more along the lines of this:

"but it does not actually occupy that "location" until we measure the position (collapsing the probability wave)." .

But the instant we look at the electron, it's path is disturbed... thanks .. I think I'm getting to understand what all this is..
However, I won't mark this thread as solved just yet. If anyone else has any ideas, please post them here...