How is the electron wavefunction determined?

[Saado]

How is the wavefunction of an electron determined? I've seen images which show that it looks like this : http://abyss.uoregon.edu/~js/images/wave_function.gif

But how do we know this?

On hyperphysic's website, it seems to say that many sine waves added together make the wave function : http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html

Could anybody clarify this

 

[Nugatory]

The wave functions are the solutions of Schrödinger's equation; if you want to know what the wave function "looks like" you have to set up and solve that equation. The sine wave (and sums of sine waves) are the solution for a free particle such as an electron hanging out in empty space.

 

[Saado]

Thank you. That helped a lot

 

[cgk]

On a related note, doing precisely this, calculating electronic wave functions (or similar quantities) of realistic physical systems like molecules and solids is the main subject of a a large branch of physics called "electronic structure theory". Techniques to do this are dealt with in theoretical condensed matter physics and quantum chemistry.

 

[PhilDSP]

There is a recently developed technique which generates an actual picture of the wave function for several electron orbitals of a hydrogen atom using composite snapshots:

http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.110.213001

Popular reporting:
http://www.foxnews.com/science/2013/05/28/amazing-first-ever-photograph-inside-hydrogen-atom/

 

[Nugatory]

There is a recently developed technique which generates an actual picture of the wave function for several electron orbitals of a hydrogen atom using composite snapshots:

http://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.110.213001

Popular reporting:
http://www.foxnews.com/science/2013/05/28/amazing-first-ever-photograph-inside-hydrogen-atom/

And the comparison between the two should be enough to turn you off from popular reporting forever... No here.

Note that an "actual picture of the wave function" is not the same thing as a "picture of the actual wave function". This isn't a criticism, as the work in question is still quite fascinatingly cool.