Why doesn't the electron have a definite position?

In summary, the conversation discusses the concept of an electron being both a wave and a particle, and the difficulty in determining its precise position due to the Heisenberg uncertainty principle. The uncertainty principle states that the more precisely we know an electron's position, the less we know about its momentum and vice versa. This is a fundamental law of nature and cannot be overcome, unless a new theory replaces the current one. Even though the electron can be described by a probability wave, it does not occupy a specific position until it is measured, which can also disturb its path. The conversation ends with a final question about whether the electron actually has a position in space, and the response points out the importance of considering discreet energy levels and the effects of measuring
  • #1
mahela007
106
0
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...
 
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  • #2
Well if we gave it a definite position, then it wouldn't really be a wave?
 
  • #3
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,[tex]\Delta x \times \Delta p \geq \frac{h}{2}[/tex] 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
 
  • #4
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).
 
  • #5
mahela007 said:
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 Schrodinger 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 Schrodinger 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 Schrodinger equation.

At first Schrodinger 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.
 
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  • #6
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.
 
  • #7
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.)
 
  • #8
mahela007 said:
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.
 
  • #9
vociferous said:
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...
 
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Related to Why doesn't the electron have a definite position?

1. Why is the position of an electron uncertain?

The uncertainty in the position of an electron is a fundamental property of quantum mechanics. According to the Heisenberg uncertainty principle, it is impossible to know both the exact position and momentum of a particle at the same time. The act of measuring the position of an electron changes its momentum, making it impossible to determine its exact position.

2. Can we ever know the exact position of an electron?

No, we cannot know the exact position of an electron due to the uncertainty principle. The best we can do is determine the probability of finding an electron at a certain location, but we can never know its exact position.

3. How does the uncertainty in the position of an electron affect its behavior?

The uncertainty in the position of an electron has a significant impact on its behavior. Since we cannot know its exact position, we can only describe its behavior in terms of probabilities. This leads to the wave-like behavior of electrons, where they can be found in multiple places at once.

4. Are there any practical applications of the uncertainty principle?

Yes, the uncertainty principle has many applications in technology, such as in the development of quantum computing and nanotechnology. It also helps us understand the behavior of particles at the atomic level and has been crucial in the development of modern physics.

5. Can the uncertainty principle be applied to larger objects, such as humans?

No, the uncertainty principle only applies to objects at the atomic and subatomic level. The effects of uncertainty are not noticeable at the macroscopic level, so it does not apply to humans or other large objects.

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