Gaussian superposition

An animation of the graph of exp[-(x-L)^2 -y^2] + exp[-(x+L)^2-y^2] as L varies from -4 to 4. Note that the point (x=0,y=0) begins and ends as a saddle point, but becomes a local maximum for small |L|.

Category:

Film & Animation

Tags:

• multivariable
• calculus

[EricEqualsMCSquared]

and the significance of this is?

[jzimba]

I uploaded it a couple of years ago so my calculus students could look at it. We were studying optimization. (The point at the center changes from a saddle to a maximum and back.)

[idoll99]

It would be much better if you let two solitons with different size collide together...Since they have very similar size, looks like they bounce back from each other which is obviously not true. Nice video anyway...

[jzimba]

Thanks! This was for a calc class, no physics implied - especially not solitons. We'd evaluated the max/min criterion as a fcn of the separation, so I wanted to show what was going on visually. I use YouTube to show videos in class. BTW, I disagree with your stmt that it is "obviously not true" that they bounce back from each other. Nor wd I say they pass thru each other. In the bosonic case, both stmts are equally devoid of meaning.

[KakHazhar]

pretty cool!

[idoll99]

cool!

[sanchezdot]

wuuuuooooooooooo  :)

[mcboi92]

kool!

[Markusqwertyuiop]

VERY NICE!