# Need help with Schrödinger and some integration!

#### Basip

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:
Related Advanced Physics Homework Help News on Phys.org

#### Matterwave

Gold Member
please use two \$-signs for latex wrappers, and two #-signs for in-line latex.

#### jtbell

Mentor
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 $\psi_2$.

#### Basip

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

Mentor
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 $\psi^*_2$?

#### Basip

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

Mentor
Generally speaking, how does one do complex conjugation?

#### jtbell

Mentor
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!