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Math Help - A question about Schrödinger's Wave Equation.

  1. #1
    Super Member Aryth's Avatar
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    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:

    \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 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?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Aryth View Post
    So, we're going over the Born interpretation of the function, and it gives rise to the normalization condition:

    \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 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 |\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
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    Super Member Aryth's Avatar
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    Ah, I see. That makes sense. I appreciate it.
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