- 9

- 0

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!

##\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: