Normalization

**ryukolink** · September 29th 2009, 07:53 PM

soooo I need to normalize this

wavefunction (x) = Ne^[(-x^2)/(2a^2)]

A is a constant, and x goes from neg. to pos. infinite..

I keep doing it over and over.. trying, but now I'm here.. sigh. Our professor is not doing a good job and to make matters worse, hes on vacation our first week in school (he lectured us once), lol.

**mr fantastic** · September 30th 2009, 12:05 AM

Originally Posted by ryukolink

soooo I need to normalize this

wavefunction (x) = Ne^[(-x^2)/(2a^2)]

A is a constant, and x goes from neg. to pos. infinite..

I keep doing it over and over.. trying, but now I'm here.. sigh. Our professor is not doing a good job and to make matters worse, hes on vacation our first week in school (he lectured us once), lol.

$\int_{- \infty}^{+ \infty} e^{- \frac{x^2}{2a^2}} \, dx = a \sqrt{2} \int_{- \infty}^{+ \infty} e^{-u^2} \, du = a \sqrt{2} \sqrt{\pi}$ (see Gaussian integral - Wikipedia, the free encyclopedia) $= a \sqrt{2 \pi}$ .

**ryukolink** · September 30th 2009, 06:04 AM

wow, I wish I had known about the gaussian integral..

k so u-sub I did that as well, couldnt integrate from there, guess I am retarded lol.

So this is the answer... (now going beyond the question)

but to find the normalizing factor I would just Divide one by this answer making it

N = 1 / [answer^(1/2)], I am correct in this assumption... I hope so cause I read it and took notes on it.

**ryukolink** · September 30th 2009, 11:33 AM

Originally Posted by mr fantastic

$\int_{- \infty}^{+ \infty} e^{- \frac{x^2}{2a^2}} \, dx = a \sqrt{2} \int_{- \infty}^{+ \infty} e^{-u^2} \, du = a \sqrt{2} \sqrt{\pi}$ (see Gaussian integral - Wikipedia, the free encyclopedia) $= a \sqrt{2 \pi}$ .

now wait a minute... we are taught that normalization is the complex conjugate of the wave function times the orig. wave function, why did you just plug in the original wave function and not multiply it out ? (obviously the integration and what not is correct.. but I got a little confused here when looking it over for a second time when I was actually not a zombie.

**mr fantastic** · September 30th 2009, 07:24 PM

Originally Posted by ryukolink

now wait a minute... we are taught that normalization is the complex conjugate of the wave function times the orig. wave function, why did you just plug in the original wave function and not multiply it out ? (obviously the integration and what not is correct.. but I got a little confused here when looking it over for a second time when I was actually not a zombie.

I asumed that you had already done that in what you posted and that your trouble was dealing with the resulting integral.

See Normalization of the wave-function

Otherwise what you posted makes no sense (to me anyway).

Originally Posted by ryukolink

wow, I wish I had known about the gaussian integral..

k so u-sub I did that as well, couldnt integrate from there, guess I am retarded lol. Mr F says: The link I posted showed how to do it. Did you read it? Otherwise it's a result that can be assumed.

So this is the answer... (now going beyond the question)

but to find the normalizing factor I would just Divide one by this answer making it

N = 1 / [answer^(1/2)], I am correct in this assumption... I hope so cause I read it and took notes on it.

..

**ryukolink** · September 30th 2009, 07:36 PM

just forget it, I got it heh

thanks for the help, as always.

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