Normalize function - quantum chemistry

[kanciara]

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

 

[vela]

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 $r$.

 

[topsquark]

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