# Thread: Normalising A given Gauss Integral with a constant coefficient

1. ## Normalising A given Gauss Integral with a constant coefficient

Dear Folks,

I need to normalise a wave function by solving for A given that

$1=A^2 \int^{\infty}_{-\infty} e^{-\frac{m\omega x^2}{\hbar}}dx$

The gauss integral is given as
$\sqrt {\pi}=\int^{\infty}_{-\infty} e^{-x^2}dx$

How do I handle the constant (mw/h)? I tried substitution but it broke down...

Thanks

2. Originally Posted by bugatti79
Dear Folks,

I need to normalise a wave function by solving for A given that

$1=A^2 \int^{\infty}_{-\infty} e^{-\frac{m\omega x^2}{\hbar}}dx$

The gauss integral is given as
$\sqrt {\pi}=\int^{\infty}_{-\infty} e^{-x^2}dx$

How do I handle the constant (mw/h)? I tried substitution but it broke down...

Thanks
Substitute $\displaystyle u = \sqrt{\frac{m \omega}{\hbar}}x$. If you need more help, please show all your work and say where you get stuck.

3. Originally Posted by mr fantastic
Substitute $\displaystyle u = \sqrt{\frac{m \omega}{\hbar}}x$. If you need more help, please show all your work and say where you get stuck.
Thanks Mr Fantastic,
See attached jpg.

4. Originally Posted by bugatti79
Thanks Mr Fantastic,
See attached jpg.
Sorry, but the last lines that begin with "I attempted" are completely wrong. If you are trying to derive the general result, I suggest you Google:

integral gaussian

or similar search string to find the correct approach.

5. I know it was completely wrong...thats what I wrote on the last line, my attempt was 'rubbish'. Sorry for bad writing!!!

I was aware of the gauss integral but I didnt know how to perform the correct substitution

Cheers