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:

[tex]\nabla^2 \equiv \Delta[/tex]

Njorl

I've always seen it point down.

Njorl

master_coda

I also usually see [itex]\nabla^2[/itex]. But [itex]\Delta[/itex] is perfectly valid.

Personally I prefer [itex]\nabla^2[/itex]. 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 [itex]\Delta[/itex] is already used enough anyway.

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

HallsofIvy

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