# A question about Schrödinger's Wave Equation.

• Jun 2nd 2009, 05:46 PM
Aryth
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?
• Jun 3rd 2009, 03:28 AM
CaptainBlack
Quote:

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
• Jun 3rd 2009, 06:18 AM
Aryth
Ah, I see. That makes sense. I appreciate it.