Normalization of wave functions (hydrogen)

GreenLRan
Messages
59
Reaction score
0

Homework Statement



Show that the (1,0,0) and (2,0,0) wave functions listed in table 7.1 are properly normalized.

http://www.geocities.com/greenlran/phtable712.jpg

Homework Equations



psi.n.l.ml.(r,theta,phi)=R.n.l.(r)THETA.l.ml.(theta)PHI.ml.(phi)

The Attempt at a Solution



To normalize a wave function you square the function and integrate it, then multiply the original function by 1 over the sqrt of the integral to make it equal 1 correct? How do i checked to see if these are normalized?
 
Physics news on Phys.org
If a wavefunction is normalised, what can you say about integral of the square of the norm of the wavefunction?
 
would it be the original wave function? or just 1? I am not exactly sure how to integrate this either...
 
It would be equal to one, since the integral over the whole space of the square of the norm of the wavefunction is equal to the probabilty of finding the particle in that space. Since we want it to be normalised, this means that this probability is equal to one.
 
Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
Back
Top