Symmetric and Antisymmetric Depiction

1. Aug 13, 2015

Davephaelon

I was looking at this excellent website this afternoon, and was puzzled by two diagrams showing the symmetric and antisymmetric wavefunctions. In the latter case the text states that the particles are far away from each other, explaining the Pauli Exclusion Principle, etc. But looking at the contour maps showing the density of the particles at a particular location, both symmetric and antisymmetric wavefunctions look identical in form, just rotated by 90 degrees from each other. Here's the page: http://galileo.phys.virginia.edu/classes/252/symmetry/Symmetry.html

There must be something perfectly obvious that I'm overlooking here. Any help would be appreciated.

2. Aug 13, 2015

Orodruin

Staff Emeritus
But this is the entire point! What is plotted is the probability density in the x1-x2-plane. Look at the two white blobs. For the symmetric case, they are located so that x1 is roughly equal to x2 inside the blobs. For the antisymmetric case, a small x1 implies a large x2 and vice versa. It is not a matter of the blobs being close to each other, it is a matter of how far away from the line x1=x2 the majoriity of the distribution is.

3. Aug 13, 2015

Davephaelon

Thank you for the response and explanation. I was away from the computer for a time, and will have to look again at the images, and text, to see exactly what you are saying.