Normalize function - quantum chemistry

  • #1
kanciara
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Homework Statement:
Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector
Relevant Equations:
f(r)=N*exp{-alpha*r}
Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector

I was just wondering if the fact that we have a vector value in our equation changes anything about the solution
 

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  • #2
vela
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Homework Statement:: Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector
Relevant Equations:: f(r)=N*exp{-alpha*r}

Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector

I was just wondering if the fact that we have a vector value in our equation changes anything about the solution
Why do you think ##r## is a vector? Make sure you're not confusing vector ##\vec r## with its magnitude ##r##.
 
  • #3
topsquark
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Homework Statement:: Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector
Relevant Equations:: f(r)=N*exp{-alpha*r}

Normalize function f(r) = Nexp{-alpha*r}
Where alpha is positive const and r is a vector

I was just wondering if the fact that we have a vector value in our equation changes anything about the solution
The argument inside the exponential needs to be a scalar, so it would have to be something like ## \alpha \cdot \textbf{r}##. It should be clear by context. I've seen ##\textbf{k} \cdot \textbf{x}## in a wavefunction but never written with a radial variable.

If it is a scalar product then you will have something like
##\int N e^{ \alpha _r r + \alpha _{ \theta } \theta + \alpha _{ \phi } \phi }## (or some such) which you should be able to separate out and integrate individually.

-Dan
 

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