So, we're going over the Born interpretation of the function, and it gives rise to the normalization condition:

[LaTeX Error: Can't write to directory]

My professor wasn't very descriptive of it, but the question I have is what does the [LaTeX Error: Can't write to directory] mean? I know it represents a volume, and in the integral it is over all space... So, what does it mean mathematically?

The [LaTeX Error: Can't write to directory] is the 3-D infinitesimal volume unit. Depending on the coordinate system you will be using it as [LaTeX Error: Can't write to directory] for Cartesian coordinates, or it could be [LaTeX Error: Can't write to directory] for spherical polar coordinates.

-Dan

__________________
"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

I see, its just not in the form I'm used to. Thanks for the help.

Physically, |ψ(r,t)|2 represents the probability density or the probability of finding the particle in the infinitesimal volume element d3 r and its integral over all space is the probability of finding the particle in all space, which = 1 because the particle is present somewhere.

Sorry if this sounds rude. But I knew the interpretation of the integral itself...

But as far as a mathematical representation of [LaTeX Error: Can't write to directory] goes, I had no idea what it implied besides the fact that it represented a volume physically. I had a feeling that it was just being used for dxdydz, etc.

But I have no experience in partial differential equations (Its a theoretical physics course, covers the basics of Schrodinger's equation), so I had never seen that operator before.

Not at all. But some others might benifit. I myself have often learned many things in this forum from such supplementary though debatably unwarranted comments.

I had that same problem too when I first came across that notation. It does look odd, doesn't it?