# When the electron prob wave spreads what happens to the electron?

#### LostConjugate

When the electron's probability wave spreads out to a macroscopic size, what happens? How does it return to a microscopic spread in the future? Does the electron gain a new probability wave?

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#### Matterwave

Gold Member
The chances that an electron's wave-function spreads to macroscopic size is infinitesimal due to the large chances of interaction.

But anyways, according to SQT (not including decoherence) the electron's wave function will collapse instantaneously back to a very sharply peaked and narrow wave function once a measurement of its position is made by any observer. This is called wave function collapse, and is not yet quite well understood. I hear decoherence is solving that problem though...I'm not too familiar with decoherence.

#### LostConjugate

So each time the electron interacts the wave function returns to some given spread? I read it can take much less than a second for an electron wave function to spread to a macroscopic size.

#### jeblack3

You can't analyze this properly in terms of just a wavefunction describing the electron. Once the electron interacts with anything, you need to consider the joint quantum state of the electron and whatever it interacted with.

#### LostConjugate

So what can we say about a free electron in a vacuum. After a few seconds it could be anywhere within an astronomical range? And what about the momentum, that spreads just as quickly, the crazy thing could be going FTL before you know it :)

#### jeblack3

I'm not sure where you're getting these figures, or if this is a joke I don't get, but momentum is conserved, so in empty space with no interactions there won't be any change to the momentum probability distribution.

#### Sillyboy

Principles of Quantum Mechanics by R.Shankar says, it takes a long time to convert it. But this book is not available at hand. So I cannot give the exact value. And I think Matterwave's explaination is good.

#### LostConjugate

5.71 through 5.86 from this PDF http://www.physics.sfsu.edu/~greensit/book.pdf [Broken]
It never explains what happens to the electron when it's function spreads to macroscopic size.

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#### DrChinese

Gold Member
Although the chances are that the probability wave will expand far away are remote, it is technically not correct to say that the wave stops spreading when it interacts with something else. Not trying to be picky here, but more address the point the OP is trying to ask about.

Any time a quantum particle is detected "here", logically it is NOT detected "there". It would be correct to say that "there" can be any possible history of the particle, including one in the distant future in a distant location. So a measurement here implies something about there, and vice versa.

If you think about it logically, the collapse of the wavefunction can be seen as defining quantum non-locality. Entanglement experiments are the usual way to see this, but it does not take 2 particles to have quantum non-locality.

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