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Explain Wave Function for a science starter


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How to explain Wave function concepts to a High School student with bear knowledge of mathematics

It's easy. Any meaningful picture contains many points - pixels, if you like. So one point (pixel) is not sufficient to describe the picture of a complex thing. But we may construct this picture point by point, OK? Each point belongs to the whole picture but is insufficient to represent it. Now, the wave function squared is the whole picture and each separate, elementary quantum mechanical "measurement" is a pixel of the whole picture. The wave function does not collapse while measurement. On the contrary, each "elementary" measurement is the information bit retrieval, if you like, necessary for description of a complex thing.

Edited by Bob_for_short
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I think that energy quantification is very difficult to understand for high school student.

How to describe this concept easily?

Commonly, we describe this concept by using light spectrum discontinuity.

But at the high school student this is not easy to understand.

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  • 2 weeks later...

How to explain Wave function concepts to a High School student with bear knowledge of mathematics

 

The wave function which is the mathematical property of wave particle duality is simply this for a beginner: All elementary particles are both particles AND waves. The next step after that is "what are they waves of"? To which the answer is, existence itself. After that, since the particles are also waves, at the sub-atomic level, an electron for instance can occupy multiple points in space simultaneously. However, whenever a particle is measured in anyway, this property of a wave "collapses". In other words, when you look at something or feel something, the particles causing that now only act as single points and not waves, for as long as you measure them in some way. However, this is only on the every day level. When scientists tried to look at how this works close up, they found that as a single measured point, the particle still acts like a wave in some way in that it appears to pop in and out of existence at different points around specific areas. In something such as an electron orbiting the nucleus, the electrons have specific places where they are most likely to "pop up". And most of the time, particles pop up in their most probable places. The most probable place for an electron to show up around a nucleus with the lowest energy level is a sphere about .529*10^-10 meters in radius. As different properties of the electron change such as the energy, the areas of the most probable places for the particle to show up change. If an electron gained energy to go to the next energy level, then its most probable place to pop up would occupy a further region away from the nucleus, taking either dumbbell shape or a double sphere. However, these are just the most probable places for the electron to show up. In reality, the place a particle could pop up is infinite, or in other words, a particle's wave function extends indefinitely through space. However, its very very unlikely that particles appear anywhere away from their most probable places. An electron could pop up at the other end of the universe, but the odds of that are approximately 1 in 10^1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000. Probably even more than that. This is why the classical world is so different, it's just not that probable for particles to pop up any sort of noticeable distance away from their most probable places to show up.

 

P.S. Random fact: In case you didn't notice, my second favorite word is "however".

Edited by steevey
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I like to think of it like this: An electron travels like a wave but hits like a particle.

 

Assume you have an electron gun here and a whole bunch of electron detectors over there.

 

Once an electron is emitted from the gun, it spreads through space like a wave. This wave is a probability wave. It tells us the odds of where the electron may be found. This, in essence, is the so-called wave function.

 

But the electron hits (is detected) only in a single location in space, like a particle. We have no idea exactly which of our many detectors will capture that electron. We can only calculate the odds of finding it at a certain detector location based on the wave function.

 

And not just electrons, but all fundamental particles, composite particles, and even atoms behave this same way.

 

Take a look at http://www.marksmodernphysics.com/ and click on Selected Animations and "Light through a Beam-Splitter" for picture of how wave functions work.

 

Hope this helps.

Edited by I ME
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However, these are just the most probable places for the electron to show up. In reality, the place a particle could pop up is infinite, or in other words, a particle's wave function extends indefinitely through space. However, its very very unlikely that particles appear anywhere away from their most probable places. An electron could pop up at the other end of the universe, but the odds of that are approximately 1 in (approaching infinity) Probably even more than that. This is why the classical world is so different, it's just not that probable for particles to pop up any sort of noticeable distance away from their most probable places to show up.

This intermittency of electron position makes it difficult to believe that electrons are actually capable of creating volume around the nucleus. How is it that atoms avoid interpenetrating each other's electron clouds if electrons are as absent as they are present? Or is it that at the speed of electrons, atomic/molecular motion are relatively slower thus making it possible but highly unlikely for an electron to teleport at the moment it is approaching the electron(s) from another molecule that it will bounce off of?

Edited by lemur
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This intermittency of electron position makes it difficult to believe that electrons are actually capable of creating volume around the nucleus. How is it that atoms avoid interpenetrating each other's electron clouds if electrons are as absent as they are present? Or is it that at the speed of electrons, atomic/molecular motion are relatively slower thus making it possible but highly unlikely for an electron to teleport at the moment it is approaching the electron(s) from another molecule that it will bounce off of?

 

Although the wave function property allows electrons to pop up pretty much anywhere, what governs them and their probable areas are a set of 4 quantum mechanical properties or numbers. These 4 properties which are the energy level, angular momentum, spin, and some kind of magnetic quantum number. Along with the fact that like charges repel each other, no two particles in the same system can have all the same 4 quantum values. This is more what separates electron's from each other in a wave or point state.

Edited by steevey
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Although the wave function property allows electrons to pop up pretty much anywhere, what governs them and their probable areas are a set of 4 quantum mechanical properties or numbers. These 4 properties which are the energy level, angular momentum, spin, and some kind of magnetic quantum number. Along with the fact that like charges repel each other, no two particles in the same system can have all the same 4 quantum values. This is more what separates electron's from each other in a wave or point state.

Ok, thanks, but what about my question of how the electron clouds of atoms/molecules prevent them from interpenetrating if the electrons are locationally intermittent?

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Ok, thanks, but what about my question of how the electron clouds of atoms/molecules prevent them from interpenetrating if the electrons are locationally intermittent?

 

Generally, particles don't inter-penetrate each other because of the different quantum numbers. However, an electron never stops being a wave either. What can happen as a result of this is entanglement (or if the particles just interact, they can become entangled). If the wave functions of separate particles overlap with certain mathematical properties and haven't been measured, then their properties are no longer determined, and so their wave functions are combined to hold the information of a single undetermined particle. But what tends to happen is this entanglement disentangles whenever its measured in any way.

Edited by steevey
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Generally, particles don't inter-penetrate each other because of the different quantum numbers. However, an electron never stops being a wave either. What can happen as a result of this is entanglement (or if the particles just interact, they can become entangled). If the wave functions of separate particles overlap with certain mathematical properties and haven't been measured, then their properties are no longer determined, and so their wave functions are combined to hold the information of a single undetermined particle. But what tends to happen is this entanglement disentangles whenever its measured in any way.

I can't tell if when you say that "particles don't inter-penetrate each other because of the different quantum numbers," you are referring to some physical reason they prevent it or if you're just referring to correlation patterns between measurements and events. By "entanglement," are you referring to chemical bonding?

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I can't tell if when you say that "particles don't inter-penetrate each other because of the different quantum numbers," you are referring to some physical reason they prevent it or if you're just referring to correlation patterns between measurements and events. By "entanglement," are you referring to chemical bonding?

 

The physical reason they don't penetrate is because they have different mathematical values as a wave or point which govern how they act. If two waves had all the same properties, they would cancel out each other's existence.

 

waves-1.jpg

 

 

 

And when I say entanglement, I'm referring to the phenomena of when two particles interact and haven't been measured since the interaction, their wave functions combine with each other so that the two particles now count as the same particle. But, when the entangled objects are measured, they become dis-entangled and return to separate particle states.

 

 

Edited by steevey
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  • 4 weeks later...

I for one would enjoy, hearing in a little more detail, how two identical things( electrons, states, atoms whatever ) are inherently prohibited from existing.

 

Because then they would be occupying the same space meaning they wouldn't actually ever exist in the same place, or as I showed, their waves would cancel out. When the electron passes through two slits in the double slit experiment, the high point in the wave crest meets the troff, or lowest point simultaneously, so it cancels out there and forms a wave pattern since the wave points are "adding" together. 1 + -1 = 0.

Edited by steevey
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