Should it be upside or downside

[MathematicalPhysicist]

how does the triangle symbol in Helmholtz Equation should be?
is it like the attach file in here.

 

[MathematicalPhysicist]

or like this attach file.

btw, can you attach more then one file in here?

 

[suyver]

If I remember correctly, then they are both the same. nabla squared is sometimes denoted as a triangle with the sharp side up.

So:

\nabla^2 \equiv \Delta

 

[Njorl]

I've always seen it point down.

Njorl

 

[master_coda]

I also usually see \nabla^2. But \Delta is perfectly valid.

Personally I prefer \nabla^2. It makes it more clear what operation you're actually performing. Plus it help avoid defining a new symbol for every single mathematical operation. And \Delta is already used enough anyway.

In the Helmholtz equation in particular \nabla^2 looks better.
\nabla^2\psi+k^2\psi=0 is more symmetric.

 

[HallsofIvy]

loop quantum gravity: note well it is \nabla^2 and \Delta that are the same not \nablaand \Delta!