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Need help with Schrödinger and some integration!

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Moved here from non-homework forum, therefore template is missing
My wave function:
##\psi_2=N_2 (4y^2-1) e^{-y^2/2}.##
Definition of some parts in the wavefunction ##y=x/a##, ##a= \left( \frac{\hbar}{mk} \right)##, ##N_2 = \sqrt{\frac{1}{8a\sqrt{\pi}}}## and x has an arrange from ##\pm 20\cdot 10^{-12}##.
Here is my integral:
##<x^2> = \int\limits_{-\infty}^{\infty}\psi_2^*x^2\psi_2dx.##
It should integrate it directly or with Hermite polynomials: http://en.wikipedia.org/wiki/Hermite_polynomials
I don't know how to do that. And I does ##\psi_2^*## mean it is conjugated? Really need some help here. I don't know how to start. If someone could help me, it would be great!
Thank you very much in advance!
 
Last edited:

Matterwave

Science Advisor
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please use two $-signs for latex wrappers, and two #-signs for in-line latex.
 

jtbell

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I don't know how to do that.
What, specifically, do you not know how to do? What to substitute for ##\psi_2##? What to substitute for ##\psi^*_2##? How to evaluate the resulting integral?

does ψ∗2\psi_2^* mean it is conjugated?
Yes, ##\psi^*_2## is the complex conjugate of ##\psi_2##.
 
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What, specifically, do you not know how to do? What to substitute for ##\psi_2##? What to substitute for ##\psi^*_2##? How to evaluate the resulting integral?



Yes, ##\psi^*_2## is the complex conjugate of ##\psi_2##.

I don't what I should substitute ##\psi^*_2## with. ##\psi_2## would I substitute with the ##\psi_2## function and Integrate for the limits ##\pm \infty## (of course ##dx##). The same would I do with ##x^2##. I would do the same with ##\psi^*_2## and at the end I would * them together. Is it correct or totally wrong?

But still I don't know how to substitue ##\psi^*_2##.
 

DrClaude

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I don't what I should substitute ##\psi^*_2## with. ##\psi_2## would I substitute with the ##\psi_2## function and Integrate for the limits ##\pm \infty## (of course ##dx##). The same would I do with ##x^2##. I would do the same with ##\psi^*_2## and at the end I would * them together. Is it correct or totally wrong?
That doesn't work: the integral of a product is not equal to the product of integrals. Try it for yourself: is ##\int x^2 dx = (\int x dx)^2## true?

But still I don't know how to substitue ##\psi^*_2##.
What is the complex conjugate of ##\psi^*_2##?
 
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That doesn't work: the integral of a product is not equal to the product of integrals. Try it for yourself: is ##\int x^2 dx = (\int x dx)^2## true?


What is the complex conjugate of ##\psi^*_2##?
I don't know what the complex conjugate og ##\psi^*_2## is. How to figure it out? I know what ##\psi_2## is.

When I know what ##\psi_2^*## is, I should just put it in the formular, insert the ##\psi_2## in the formular, find the product and then integrate, am I right?

But what is the complex conjugate of ##\psi_2##? How to figure it out? What is ##\psi_2^*## equal with when I know ##\psi_2##? But in this case ... is ##\psi^*_2 =\psi^2##?
 
Last edited:

DrClaude

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Generally speaking, how does one do complex conjugation?
 

jtbell

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But in this case ... is ##\psi^*_2 =\psi^2##?
No, but if you make a small change to the right side it will be correct!
 

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