Normalising A given Gauss Integral with a constant coefficient

**bugatti79** · November 12th 2010, 03:02 AM

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

**mr fantastic** · November 12th 2010, 03:08 AM

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.

**bugatti79** · November 12th 2010, 11:52 AM

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.

**mr fantastic** · November 12th 2010, 12:56 PM

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.

**bugatti79** · November 12th 2010, 02:56 PM

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

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