# Thread: A question about Schrödinger's Wave Equation.

1. ## A question about Schrödinger's Wave Equation.

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

$\displaystyle \int |\Psi (\bold{r}, t)|^2 ~d^3\bold{r} = 1$

My professor wasn't very descriptive of it, but the question I have is what does the $\displaystyle d^3\bold{r}$ mean? I know it represents a volume, and in the integral it is over all space... So, what does it mean mathematically?

2. Originally Posted by Aryth
So, we're going over the Born interpretation of the function, and it gives rise to the normalization condition:

$\displaystyle \int |\Psi (\bold{r}, t)|^2 ~d^3\bold{r} = 1$

My professor wasn't very descriptive of it, but the question I have is what does the $\displaystyle d^3\bold{r}$ mean? I know it represents a volume, and in the integral it is over all space... So, what does it mean mathematically?
It means the particle is somewhere, it is the integral of what is essentially a probability density over all space. You are normalising the wave function so that $\displaystyle |\Psi (\bold{r}, t)|^2$ may be interpreted as a pdf (possibly in the sense of a generalised function/density, but that's just the way physics works).

CB

3. Ah, I see. That makes sense. I appreciate it.