# Standing wave

Gold Member
Can this animation http://en.wikipedia.org/wiki/File:GravitationalWave_PlusPolarization.gif be a good representation of a standing wave in Hydrogen?
If the wave rotated on the normal direction could then be a representation of the probability cloud in QM?
Can you give me a link whre to learn how, with which technique they get a picture of an atom of H?

## Answers and Replies

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Nugatory
Mentor
Can this animation http://en.wikipedia.org/wiki/File:GravitationalWave_PlusPolarization.gif be a good representation of a standing wave in Hydrogen?
No, it's a picture of something completely different. One very big hint that it has nothing to do with quantum mechanics is that each little moving dot in the picture represents a particle - and if you've heard it once you've heard it 83 bazillion times here - in quantum mechanics particles are not like little dots that have a position and move around.

Can you give me a link where to learn how, with which technique they get a picture of an atom of H?
The technique we use is to write down the Schrodinger equation for an electron in a central potential, and solve it. The solution is a function that describes the probability amplitude for the electron being localized within a particular region around the nucleus. Given this, we can draw a picture just by coloring all the points where the probability amplitude squared is greater than some value - that will give us the shape of the region within the electron will be found with a given probability.

Googling for "hydrogen atom solution schrodinger equation" finds many hits, although as the first one from hyperphysics says, "The solution of the Schrodinger equation for the hydrogen atom is a formidable mathematical problem....", which is a polite way of saying that there's no substitute for actually learning enough math to follow the solution. It's within the reach of any second-year class of differential equations.

1 person
Gold Member
The technique we use is to write down the Schrodinger equation.
Thanks, Nugatory, I was wondering if it is possible with modern technology (and microscopes) to scan and get sort of a picture of an atom of hydrogen.

Gold Member
Thanks a lot, Bill, that is what I was looking for. Can you comment on the ground state?