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Old 05-14-2012, 01:24 PM #1
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Default laser profile and a hydrogen atom

a quick question, did a quick search and did not find much, but why is the model for a hydrogen atom's electron "probability cloud" at different energy states, the same a the profile for a Gaussian mode profile for a laser? Just something that's been bugging me for a bit, I figure this would be the right place to learn why. in case I made it confusing, sorry, but the shapes on the proposed models of an electron cloud in a atom, make the same shapes as the beam profiles. for eg. hydrogen atom with an orbital of 2,0,0 is the same as tem10, 3,0,0=tem20, 4,0,0=tem 30 not all of the shapes can line up but their is a pattern, And not knowing to much about the math of a wave function, is not helping me :P To make it any weirder, if I take a glass full of water and tap the surface its sitting on, I get the same wave patterns that have more modes or less modes depending on the force applied.



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Old 05-14-2012, 03:50 PM #2
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Default Re: laser profile and a hydrogen atom

That's actually... really interesting. Now I am curious too. I have no answer for you.

However, it may have to do with the constraints on standing waves?
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Old 05-14-2012, 05:37 PM #3
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Default Re: laser profile and a hydrogen atom

Tasty, crusty, delicious, warm pie!

It's amazing how many things are based off of circles.
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Old 05-14-2012, 07:15 PM #4
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Default Re: laser profile and a hydrogen atom

Quote:
Originally Posted by BShanahan14rulz View Post
Tasty, crusty, delicious, warm pie!

It's amazing how many things are based off of circles.
yes indeed, though you just made me even more mystified :P Be funny to come up with math to predict the badgap energy required bump an electron to a higher state buy tapping a table with a glass of water :P
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Old 05-14-2012, 10:13 PM #5
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Default Re: laser profile and a hydrogen atom

as above, so below - old hermetic wisdom
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Old 05-15-2012, 12:25 AM #6
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Default Re: laser profile and a hydrogen atom

Quote:
Originally Posted by TheReddish View Post
a quick question, did a quick search and did not find much, but why is the model for a hydrogen atom's electron "probability cloud" at different energy states, the same a the profile for a Gaussian mode profile for a laser? Just something that's been bugging me for a bit, I figure this would be the right place to learn why. in case I made it confusing, sorry, but the shapes on the proposed models of an electron cloud in a atom, make the same shapes as the beam profiles. for eg. hydrogen atom with an orbital of 2,0,0 is the same as tem10, 3,0,0=tem20, 4,0,0=tem 30 not all of the shapes can line up but their is a pattern, And not knowing to much about the math of a wave function, is not helping me :P To make it any weirder, if I take a glass full of water and tap the surface its sitting on, I get the same wave patterns that have more modes or less modes depending on the force applied.
Here's some quick fast educated hypothesizing (kinda busy atm, but this is interesting):

From Wikipedia (Atomic orbital - Wikipedia, the free encyclopedia)

Quote:
Wave-like properties

The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency.
The electrons are never in a single point location, although the probability of interacting with the electron at a single point can be found from the wave function of the electron.

Since the electrons possess many wave-like properties, the same Gaussian mathematics that apply to photons (which also have many wave-like properties) would apply to them by my logic. Waves are waves.

From the same article:

Quote:
The shapes of atomic orbitals can be understood qualitatively by considering the analogous case of standing waves on a circular drum.
This video has been posted here before, I consider it one of the very best simple explanations of wave behavior that I've ever seen. It doesn't include much math, so the reason I'm posting it is because it talks about the many similarities between ALL waves, regardless of the materials or particles involved:

http://techchannel.att.com/play-vide...-Wave-Behavior
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Old 05-15-2012, 01:45 PM #7
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Default Re: laser profile and a hydrogen atom

so nice vid, my question is this, notice how my analog was the glass of water, and the shaped of the waves start in the center and move out like a drop of rain hitting a lake. so are EM waves round? or a tube would be a better analogy than a circle, this case. like a slinky.
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Old 05-15-2012, 02:40 PM #8
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Default Re: laser profile and a hydrogen atom

All waves are inherently omnidirectional, that's why they spread out from the point of disturbance in a circular shape (it's actually a spherical shape since the forces spread out in ALL directions, but with a 2-dimensional surface like the surface of water you see only a circle, a 2-dimensional slice of the sphere of influence..). In order to get them to travel in a specific direction, conditions must be created which form a specific path. This can be done many ways, but the most common are by creating a path as if it were a roadway between points, such as a wire or waveguide (think fiber-optics) or slinky, or the waves need to be focused in a specific direction at or near the point of origin, such as we see with beam antennas (for radio) and lasers. With the former the pathway can be complex, with many twists and turns, with the latter the pathway can only be a straight line from the source. The beam can then be directed further with reflective devices.

Also, there are multiple dimensions to any wave. When you're looking at a wave on the surface of the water, you are seeing the result of both longitudinal and transverse motion. Notice that lasers have longitudinal and transverse modes.. see a similarity there? Same with electrons in an electron cloud: longitudinal and transverse motion.

I'm not an expert in Gaussian mathematics (or any mathematics for that matter..) I only know enough about it to get myself into trouble most of the time.. but I think the root of your original question lies with the fact that ALL waves behave similarly, therefore things like mode shapes will be found throughout the world of waves. It just happens that lasers provide a VERY visible firsthand reference to them.
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Old 05-15-2012, 03:24 PM #9
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Default Re: laser profile and a hydrogen atom

Yes and the still trying to visualize the transverse E movement and then the transverse M movement with then the longitudinal waves in the added the picture gets messy But thanks for the info, you have been most informative.

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