Identical bosons vs. fermions in square potential well

[bobshae]

The following Wolfram web page shows the probability density functions for two identical bosons in a square potential well. It also shows the probability density for two identical fermions.

http://demonstrations.wolfram.com/WaveFunctionsOfIdenticalParticles/

So it appears that each is just a 90 degree rotation of the other. That doesn't seem correct. If Bosons can share the same state, shouldn't their lowest state just be a single blob in the middle (per the ground state for a single particle)? I know that quantum mechanics is very non-intuitive, so I'm probably missing something. Please help to explain this. Thank you.

--Bob

 

[Avodyne]

The sliders at the top tell you the individual states. The starting point is one particle in the ground state (n=1) and one in the first excited state (n=2). For fermions, antisymmetrizing these does give the ground state, but for bosons, you would need n=1 for both, which would give a single blob in the middle.

 

[bobshae]

The sliders at the top tell you the individual states. The starting point is one particle in the ground state (n=1) and one in the first excited state (n=2). For fermions, antisymmetrizing these does give the ground state, but for bosons, you would need n=1 for both, which would give a single blob in the middle.

Ah I see. Thank you.