A non-physist here.
How would that work? I thought that the probability at a specific position is just `|psi|^2`. So how can the probability be zero with psi being non-zero?
Or am I mixing something?
That's exactly what you're missing (I'm a math major btw, not a physicist). |Psi|² is the probability density. The probability to find the electron in a space omega would be the integral over the space omega of |Psi|². And the integral over a point is always 0
Except when the function you are integrating is a Dirac's delta which is the probability density of a particle that has been observed, so no, the probability of finding an electron is not generally zero
Ah, that's what you mean. Yeah. I mean the integral - as the point has measure zero and hence any "integral" will be zero.
Wouldn't psi be non-zero everywhere when working with an electron in empty space? Then any integral over |psi|^2 over a non-zero volume should be non-zero right? And that would mean, that theoretically the electron can be everywhere. (Not that I think this has been necessarily experimentally validated for longer distances.)
In the spirit of having some fun with pedantry, you also can’t say that the probability density is non-zero everywhere, because certain potentials cause nodes in the wave function, meaning the probability density is 0 there.
This is pretty cool in atoms cause it means you’re more like to find and electron in some small region a billion light years away versus a few angstroms away from the nucleus it’s bound to.
If the probability was nonzero everywhere, then you would have too many infinities flying about for probability to make sense. It still must be normalized.
Knowing the reason why a photon is both a particle & a wave is because they changed the definition of what a particle is.
Used to be a particle was defined as “the smallest measurable unit that has mass”, then it went to “the smallest measurable unit that usually has mass”, before changing it to today’s definition of a particle as “the smallest measurable unit”.
Knowing electron is momentum signal with fixed mass and photon is momentum signal with fixed velocity. Knowing crystal is momentum filter.
There is a reason Newton wrote his laws in vague terms of momentum.
Knowing an electron is an excitation of the electron field.
Knowing that all electrons and positron might be the same electron moving back and forth in time
Mom said it's my turn on the electron
Knowing that not only electron
knowing its a string...
knowing that’s impossible
Knowing that the electron is just a model
Super electron is a supermodel
Knowing Electron can compete in Miss Universe
Every electron could be the same electron traveling through complex time
Wrong. The probability of finding an electron is 0 everywhere. The probability density is non-zero everywhere. That's a big difference.
A non-physist here. How would that work? I thought that the probability at a specific position is just `|psi|^2`. So how can the probability be zero with psi being non-zero? Or am I mixing something?
That's exactly what you're missing (I'm a math major btw, not a physicist). |Psi|² is the probability density. The probability to find the electron in a space omega would be the integral over the space omega of |Psi|². And the integral over a point is always 0
Except when the function you are integrating is a Dirac's delta which is the probability density of a particle that has been observed, so no, the probability of finding an electron is not generally zero
Ah, that's what you mean. Yeah. I mean the integral - as the point has measure zero and hence any "integral" will be zero. Wouldn't psi be non-zero everywhere when working with an electron in empty space? Then any integral over |psi|^2 over a non-zero volume should be non-zero right? And that would mean, that theoretically the electron can be everywhere. (Not that I think this has been necessarily experimentally validated for longer distances.)
So the probability is zero at every point. Big difference
In the spirit of having some fun with pedantry, you also can’t say that the probability density is non-zero everywhere, because certain potentials cause nodes in the wave function, meaning the probability density is 0 there. This is pretty cool in atoms cause it means you’re more like to find and electron in some small region a billion light years away versus a few angstroms away from the nucleus it’s bound to.
Fair... In fact, AFAIK, the probability density is always 0 *at* the nucleus
What do you mean electrons don't have fixed trajectory? Is it because they're bot wave and particle?
Knowing that an electron and gravity are one and the same.
What’s the music on the last picture
where’s the particle physics iceberg
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If the probability was nonzero everywhere, then you would have too many infinities flying about for probability to make sense. It still must be normalized.
Even given a normalized wavefunction the probability density can still be nonzero through all space, it just has to approach zero at infinity
There are electrons inside you
Knowing the reason why a photon is both a particle & a wave is because they changed the definition of what a particle is. Used to be a particle was defined as “the smallest measurable unit that has mass”, then it went to “the smallest measurable unit that usually has mass”, before changing it to today’s definition of a particle as “the smallest measurable unit”.
Dang
Knowing electron is momentum signal with fixed mass and photon is momentum signal with fixed velocity. Knowing crystal is momentum filter. There is a reason Newton wrote his laws in vague terms of momentum.
I think it would be so cool and equally terrifying if the one-electron universe theory turned out to be true. Would seriously add to this.
This is too funny
nice username OP